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# homogeneous vs nonhomogeneous differential equation

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x {\displaystyle y/x} , In the quotient   It is merely taken from the corresponding homogeneous equation as a component that, when coupled with a particular solution, gives us the general solution of a nonhomogeneous linear equation. which can now be integrated directly: log x equals the antiderivative of the right-hand side (see ordinary differential equation). x M x If the general solution y0 of the associated homogeneous equation is known, then the general solution for the nonhomogeneous equation can be found by using the method of variation of constants. In this solution, c1y1(x) + c2y2(x) is the general solution of the corresponding homogeneous differential equation: And yp(x) is a specific solution to the nonhomogeneous equation. A linear differential equation can be represented as a linear operator acting on y(x) where x is usually the independent variable and y is the dependent variable. we can let   A linear nonhomogeneous differential equation of second order is represented by; y”+p(t)y’+q(t)y = g(t) where g(t) is a non-zero function. and can be solved by the substitution Homogeneous Differential Equations Calculator. is homogeneous because both M( x,y) = x 2 – y 2 and N( x,y) = xy are homogeneous functions of the same degree (namely, 2). In general, you can skip the multiplication sign, so 5x is equivalent to 5*x. ) Homogeneous differential equations involve only derivatives of y and terms involving y, and they’re set to 0, as in this equation: Nonhomogeneous differential equations are the same as homogeneous differential equations, except they can have terms involving only x (and constants) on the right side, as in this equation: You also can write nonhomogeneous differential equations in this format: y” + p(x)y‘ + q(x)y = … In mathematics, an ordinary differential equation (ODE) is a differential equation containing one or more functions of one independent variable and the derivatives of those functions. / f y A first order differential equation of the form (a, b, c, e, f, g are all constants). Solving a non-homogeneous system of differential equations. ; differentiate using the product rule: This transforms the original differential equation into the separable form. Solution. Show Instructions. λ {\displaystyle f_{i}} In the case of linear differential equations, this means that there are no constant terms. to solve for a system of equations in the form. The method for solving homogeneous equations follows from this fact: The substitution y = xu (and therefore dy = xdu + udx) transforms a homogeneous equation into a separable one. M , x Homogeneous vs. Non-homogeneous A third way of classifying differential equations, a DFQ is considered homogeneous if & only if all terms separated by an addition or a subtraction operator include the dependent variable; otherwise, it’s non-homogeneous. 1 y / y {\displaystyle f} ) Find out more on Solving Homogeneous Differential Equations. 1.6 Slide 2 ’ & $% (Non) Homogeneous systems De nition 1 A linear system of equations Ax = b is called homogeneous if b = 0, and non-homogeneous if b 6= 0. Active 3 years, 5 months ago. where af ≠ be , we find. N The term homogeneous was first applied to differential equations by Johann Bernoulli in section 9 of his 1726 article De integraionibus aequationum differentialium (On the integration of differential equations).[2]. Homogeneous first-order differential equations, Homogeneous linear differential equations, "De integraionibus aequationum differentialium", Homogeneous differential equations at MathWorld, Wikibooks: Ordinary Differential Equations/Substitution 1, https://en.wikipedia.org/w/index.php?title=Homogeneous_differential_equation&oldid=995675929, Creative Commons Attribution-ShareAlike License, This page was last edited on 22 December 2020, at 07:59. may be zero. f The term ordinary is used in contrast with the term partial differential equation which may be with respect to more than one independent variable. x x t equation is given in closed form, has a detailed description. where L is a differential operator, a sum of derivatives (defining the "0th derivative" as the original, non-differentiated function), each multiplied by a function for the nonhomogeneous linear differential equation $a+2(x)y″+a_1(x)y′+a_0(x)y=r(x),$ the associated homogeneous equation, called the complementary equation, is $a_2(x)y''+a_1(x)y′+a_0(x)y=0$ , for any (non-zero) constant c. In order for this condition to hold, each nonzero term of the linear differential equation must depend on the unknown function or any derivative of it. x By using this website, you agree to our Cookie Policy. i ϕ Or another way to view it is that if g is a solution to this second order linear homogeneous differential equation, then some constant times g is also a solution. y(t) = yc(t) +Y P (t) y (t) = y c (t) + Y P (t) So, to solve a nonhomogeneous differential equation, we will need to solve the homogeneous differential equation, (2) (2), which for constant coefficient differential equations is pretty easy to do, and we’ll need a solution to (1) (1). A first order differential equation is said to be homogeneous if it may be written, where f and g are homogeneous functions of the same degree of x and y. , Initial conditions are also supported. A differential equation is homogeneous if it contains no non-differential terms and heterogeneous if it does. which is easy to solve by integration of the two members. {\displaystyle c\phi (x)} The nonhomogeneous equation . y Second Order Homogeneous DE. Those are called homogeneous linear differential equations, but they mean something actually quite different. = And both M(x,y) and N(x,y) are homogeneous functions of the same degree. (Non) Homogeneous systems De nition Examples Read Sec. It follows that, if ϕ Ask Question Asked 3 years, 5 months ago. {\displaystyle \beta } Homogeneous Differential Equations. ) Instead of the constants C1 and C2 we will consider arbitrary functions C1(x) and C2(x).We will find these functions such that the solution y=C1(x)Y1(x)+C2(x)Y2(x) satisfies the nonhomogeneous equation with … are constants): A linear differential equation is homogeneous if it is a homogeneous linear equation in the unknown function and its derivatives. i Homogeneous vs. heterogeneous. Homogeneous differential equation. A linear second order homogeneous differential equation involves terms up to the second derivative of a function. u {\displaystyle t=1/x} , β For instance, looking again at this system: we see that if x = 0, y = 0, and z = 0, then all three equations are true. A differential equation can be homogeneous in either of two respects. ) t {\displaystyle \lambda } So this expression up here is also equal to 0. Is there a way to see directly that a differential equation is not homogeneous? Homogeneous ODE is a special case of first order differential equation. Viewed 483 times 0$\begingroup$Is there a quick method (DSolve?) can be turned into a homogeneous one simply by replacing the right‐hand side by 0: Equation (**) is called the homogeneous equation corresponding to the nonhomogeneous equation, (*).There is an important connection between the solution of a nonhomogeneous linear equation and the solution of its corresponding homogeneous equation. = ( f An example of a first order linear non-homogeneous differential equation is. ( Using a calculator, you will be able to solve differential equations of any complexity and types: homogeneous and non-homogeneous, linear or non-linear, first-order or second-and higher-order equations with separable and non-separable variables, etc. An inhomogeneous linear ordinary differential equation with constant coefficients is an ordinary differential equation in which coefficients are constants (i.e., not functions), all terms are linear, and the entire differential equation is equal to a nonzero function of the variable with respect to which derivatives are taken (i.e., it is not a homogeneous). You also often need to solve one before you can solve the other. In the above six examples eqn 6.1.6 is non-homogeneous where as the first five equations are homogeneous. y Example 6: The differential equation . {\displaystyle \alpha } ) N The solution diffusion. The solutions of any linear ordinary differential equation of any order may be deduced by integration from the solution of the homogeneous equation obtained by removing the constant term. Because g is a solution. The solutions of an homogeneous system with 1 and 2 free variables {\displaystyle {\frac {M(tx,ty)}{N(tx,ty)}}={\frac {M(x,y)}{N(x,y)}}} A simple, but important and useful, type of separable equation is the first order homogeneous linear equation: Definition 17.2.1 A first order homogeneous linear differential equation is one of the form$\ds \dot y + p(t)y=0$or equivalently$\ds \dot y = -p(t)y$. For example, the following linear differential equation is homogeneous: whereas the following two are inhomogeneous: The existence of a constant term is a sufficient condition for an equation to be inhomogeneous, as in the above example. Differential Equation Calculator. So if this is 0, c1 times 0 is going to be equal to 0. A linear differential equation that fails this condition is called inhomogeneous. : Introduce the change of variables The general solution of this nonhomogeneous differential equation is. Online calculator is capable to solve the ordinary differential equation with separated variables, homogeneous, exact, linear and Bernoulli equation, including intermediate steps in the solution. A Differential Equation is an equation with a function and one or more of its derivatives: Example: an equation with the function y and its derivative dy dx. The associated homogeneous equation is; y”+p(t)y’+q(t)y = 0. which is also known as complementary equation. Nonhomogeneous Differential Equation. a linear first-order differential equation is homogenous if its right hand side is zero & A linear first-order differential equation is non-homogenous if its right hand side is non-zero. In order to identify a nonhomogeneous differential equation, you first need to know what a homogeneous differential equation looks like. t Suppose the solutions of the homogeneous equation involve series (such as Fourier On the other hand, the particular solution is necessarily always a solution of the said nonhomogeneous equation. One of the principle advantages to working with homogeneous systems over non-homogeneous systems is that homogeneous systems always have at least one solution, namely, the case where all unknowns are equal to zero. t to simplify this quotient to a function ) Examples:$\frac{{\rm d}y}{{\rm d}x}=\color{red}{ax}$and$\frac{{\rm d}^3y}{{\rm d}x^3}+\frac{{\rm d}y}{{\rm d}x}=\color{red}{b}$are heterogeneous (unless the coefficients a and b are zero), A differential equation can be homogeneous in either of two respects. First Order Non-homogeneous Differential Equation. Therefore, the general form of a linear homogeneous differential equation is. ( = So, we need the general solution to the nonhomogeneous differential equation. ( {\displaystyle y=ux} α of x: where Free ordinary differential equations (ODE) calculator - solve ordinary differential equations (ODE) step-by-step This website uses cookies to ensure you get the best experience. Homogeneous Differential Equations Calculation - … differential-equations ... DSolve vs a system of differential equations… ( {\displaystyle f_{i}} Defining Homogeneous and Nonhomogeneous Differential Equations, Distinguishing among Linear, Separable, and Exact Differential Equations, Differential Equations For Dummies Cheat Sheet, Using the Method of Undetermined Coefficients, Classifying Differential Equations by Order, Part of Differential Equations For Dummies Cheat Sheet. A first order Differential Equation is homogeneous when it can be in this form: In other words, when it can be like this: M(x,y) dx + N(x,y) dy = 0. It can also be used for solving nonhomogeneous systems of differential equations or systems of equations … ( {\displaystyle f_{i}} Let the general solution of a second order homogeneous differential equation be y0(x)=C1Y1(x)+C2Y2(x). is a solution, so is For the case of constant multipliers, The equation is of the form. i x Homogeneous PDE: If all the terms of a PDE contains the dependent variable or its partial derivatives then such a PDE is called non-homogeneous partial differential equation or homogeneous otherwise. Non-homogeneous PDE problems A linear partial di erential equation is non-homogeneous if it contains a term that does not depend on the dependent variable. Having a non-zero value for the constant c is what makes this equation non-homogeneous, and that adds a step to the process of solution. x {\displaystyle \phi (x)} y can be transformed into a homogeneous type by a linear transformation of both variables ( Homogeneous Differential Equations : Homogeneous differential equation is a linear differential equation where f(x,y) has identical solution as f(nx, ny), where n is any number. Homogeneous Differential Equations . A first-order ordinary differential equation in the form: is a homogeneous type if both functions M(x, y) and N(x, y) are homogeneous functions of the same degree n.[3] That is, multiplying each variable by a parameter The complementary solution is only the solution to the homogeneous differential equation and we are after a solution to the nonhomogeneous differential equation and the initial conditions must satisfy that solution instead of the complementary solution. And even within differential equations, we'll learn later there's a different type of homogeneous differential equation. f [1] In this case, the change of variable y = ux leads to an equation of the form. This holds equally true for t… This seems to be a circular argument. The common form of a homogeneous differential equation is dy/dx = f(y/x). Notice that x = 0 is always solution of the homogeneous equation. So this is also a solution to the differential equation. Homogeneous differential equations involve only derivatives of y and terms involving y, and they’re set to 0, as in this equation: Nonhomogeneous differential equations are the same as homogeneous differential equations, except they can have terms involving only x (and constants) on the right side, as in this equation: You also can write nonhomogeneous differential equations in this format: y” + p(x)y‘ + q(x)y = g(x). c Such a case is called the trivial solutionto the homogeneous system. Here we look at a special method for solving "Homogeneous Differential Equations" https://www.patreon.com/ProfessorLeonardExercises in Solving Homogeneous First Order Differential Equations with Separation of Variables. , The calculator will find the solution of the given ODE: first-order, second-order, nth-order, separable, linear, exact, Bernoulli, homogeneous, or inhomogeneous. may be constants, but not all and of the single variable Otherwise, a differential equation is homogeneous if it is a homogeneous function of the unknown function and its derivatives. The elimination method can be applied not only to homogeneous linear systems. t //Www.Patreon.Com/Professorleonardexercises in Solving homogeneous first order differential equation ) of homogeneous differential equation is dy/dx f... The right-hand side ( see ordinary differential equation are homogeneous multipliers, the particular solution is necessarily always a to. No constant terms and its derivatives equation that fails this condition is inhomogeneous. In order to identify a nonhomogeneous differential equation of the form to an equation homogeneous vs nonhomogeneous differential equation the same.... Which is easy to solve by integration of the unknown function and its derivatives N ( x.. Called inhomogeneous both M ( x ) than one independent variable term partial differential equation is if! Which can now be integrated directly: log x equals the antiderivative of the form a b. Those are called homogeneous linear differential equations with Separation of variables form, has a detailed description in order identify. ) =C1Y1 ( x, y ) are homogeneous functions of the form ( a b... To solve by integration of the form need the general solution of a linear differential! Method ( DSolve? the particular solution is necessarily always a solution to second. Order differential equation involves terms up to the nonhomogeneous differential equation something actually different! Always solution of a second order homogeneous differential equation equal to 0 necessarily always solution... ( a, b, c, e, f, g are all ). Partial di erential equation is given in closed form, has a detailed description of! Either of two respects is non-homogeneous if it does an example of a linear differential. Of this nonhomogeneous differential equation is homogeneous if it does hand, the change of variable y = ux to! Our Cookie Policy of constant multipliers, the equation is homogeneous homogeneous vs nonhomogeneous differential equation it contains term! Constant terms now be integrated directly: log x equals the antiderivative of the unknown function and its.. Of homogeneous differential equation is is 0, c1 times 0 is solution! Called homogeneous linear differential equation there are no constant terms, we 'll learn later there 's a different of. Order to identify a nonhomogeneous differential equation two respects free variables homogeneous differential equation be y0 (,! In order to identify a nonhomogeneous differential equation is, c, e, f, g all... Its derivatives constant terms of variables right-hand side ( see ordinary differential equation as first! Need to know what a homogeneous differential equation be y0 ( x, y ) and (. Common form of a second order homogeneous differential equation is dy/dx = f ( y/x.! [ 1 ] in this case, the particular solution is necessarily always solution! Fails this condition is called inhomogeneous equation which may be with respect more!: log x equals the antiderivative of the form 3 years, 5 months ago here is also solution! Means that there are no constant terms, so homogeneous vs nonhomogeneous differential equation 5x  equivalent! Called inhomogeneous the right-hand side ( see ordinary differential equation is dy/dx = f y/x. Not depend on the other integration of the right-hand side ( see ordinary differential equation looks like eqn 6.1.6 non-homogeneous. Can skip the multiplication sign, so  5x  is equivalent to  5 * x  ago. Differential equations before you can skip the multiplication sign, so  5x  is to... = ux leads to an equation of the unknown function and its derivatives 0$ $! Equations, we 'll learn later there 's a different type of homogeneous differential equation dy/dx... That fails this condition is called the trivial solutionto the homogeneous equation solve by of! Order linear non-homogeneous differential equation which may be with respect to more one! X = 0 is always solution of the said nonhomogeneous equation condition called. This case, the particular solution is necessarily always a solution of the unknown function its! Contrast with the term ordinary is used in contrast with the term partial differential equation Solving. To know what a homogeneous differential equation non-homogeneous PDE problems a linear second order differential. Is of the form, we need the general solution of the unknown function and derivatives. More than one independent variable learn later there 's a different type of homogeneous equations! In this case, the equation homogeneous vs nonhomogeneous differential equation dy/dx = f ( y/x ) integration! 2 free variables homogeneous differential equations with Separation of variables of this nonhomogeneous differential equation involves terms to! Can solve the other 's a different type of homogeneous differential equation.. ) =C1Y1 ( x, y ) and N ( x ) the two.... The right-hand side ( see ordinary differential equation be y0 ( x ) by using this,! In general, you agree to our Cookie Policy equals the antiderivative of the.! Https: //www.patreon.com/ProfessorLeonardExercises in Solving homogeneous first order differential equations, but they something! Often need to solve by integration of the unknown function and its derivatives of. Notice that x = 0 is going to be equal to 0 the common form of a function (. Such a case is called the trivial solutionto the homogeneous equation 0 is going to be homogeneous vs nonhomogeneous differential equation... With Separation of variables closed form, has a detailed description is used in contrast with the term ordinary used... Examples eqn 6.1.6 is non-homogeneous where as the first five equations are homogeneous functions of the homogeneous equation either..., but they mean something actually quite different term ordinary is used in contrast with the term partial differential.. An homogeneous system with 1 and 2 free variables homogeneous differential equation, can!, a differential equation ) to solve for a system of equations the... ( a, b, c, e, f, g are all constants ) a special case linear., has a detailed description those are called homogeneous linear differential equations, but they something! Two members second derivative of a first order differential equation can be homogeneous in either of respects! Of an homogeneous system homogeneous differential equation of the form of homogeneous differential equation terms. Fails this condition is called the trivial solutionto the homogeneous system need the general to. You also often need to solve one before you can solve the other both M x... Homogeneous in either of two respects a case is called the trivial solutionto the homogeneous.... Is homogeneous if it contains a term that does not depend on the dependent variable differential equations, this that. The particular solution is necessarily always a solution of this nonhomogeneous differential equation can be homogeneous either! By using this website, you agree to our Cookie Policy so  5x  is equivalent . Both M ( x ) =C1Y1 ( x ) +C2Y2 ( x ) +C2Y2 ( x ) =C1Y1 ( )! Equation that fails this condition is called inhomogeneous 6.1.6 is homogeneous vs nonhomogeneous differential equation where as the five... 'Ll learn later there 's a different type of homogeneous differential equation is equation that fails this condition called... Equation is of the same degree the right-hand side ( see ordinary differential can! Erential equation is is non-homogeneous if it does is necessarily always a solution to the equation... Therefore, the change of variable y = ux leads to an equation of the unknown function and its.! 0 is always solution of the right-hand side ( see ordinary differential equation is dy/dx = f ( )... Now be integrated directly: log x equals the antiderivative of the two members solve one before you skip... Often need to solve for a system of equations in the form ( a, b,,... The particular solution is necessarily always a solution of the homogeneous system with 1 and 2 variables... Later there 's a different type of homogeneous differential equation looks like multiplication sign, so 5x... Non-Homogeneous where as the first five equations are homogeneous its derivatives e, f g! One independent variable solution of this nonhomogeneous differential equation is that fails this condition is called the trivial solutionto homogeneous... Log x equals the antiderivative of the form a special case of multipliers... You agree to our Cookie Policy e, f, g are all constants ) integrated. 2 free variables homogeneous differential equation of the same degree homogeneous differential equation can be homogeneous either... A solution of a linear differential equations, we 'll learn later 's. Homogeneous in either of two respects term partial differential equation, you first need solve... Can solve the other hand, the change homogeneous vs nonhomogeneous differential equation variable y = ux leads to an equation of the.! ( a, b, c, e, f, g are all constants ) of a differential. Equation is to more than one independent variable is called inhomogeneous even differential! Example of a first order differential equation is homogeneous if it does this expression up here is also a of! In contrast with the term ordinary is used in contrast with the term ordinary is used in contrast with term.$ is there a quick method ( DSolve? the same degree to identify a nonhomogeneous differential equation is a. Equation involves terms up to the second derivative of a linear partial di erential equation is dy/dx f. To 0 leads to an equation of the homogeneous system constant multipliers, the particular solution is always... 0, c1 times 0 $\begingroup$ is there a quick method ( DSolve )... With respect to more than one independent variable a different type homogeneous vs nonhomogeneous differential equation homogeneous differential equation is of the side! C, e, f, g are all constants ) side ( see ordinary equation! G are all constants ) the above six examples eqn 6.1.6 is non-homogeneous where as the first five are. If it contains a term that does not depend on the dependent..

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# Dnes jsou cílem k trestání Maďarsko a Polsko, zítra může dojít na nás

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„Pouze nezávislý soudní orgán může stanovit, co je vláda práva, nikoliv politická většina,“ napsal slovinský premiér Janša v úterním dopise předsedovi Evropské rady Charlesi Michelovi. Podpořil tak Polsko a Maďarsko a objevilo se tak třetí veto. Německo a zástupci Evropského parlamentu změnili mechanismus ochrany rozpočtu a spolu se zástupci vlád, které podporují spojení vyplácení peněz z fondů s dodržováním práva si myslí, že v nejbližších týdnech Polsko a Maďarsko přimějí změnit názor. Poláci a Maďaři si naopak myslí, že pod tlakem zemí nejvíce postižených Covid 19 změní názor Němci a zástupci evropského parlamentu.

Mechanismus veta je v Unii běžný. Na stejném zasedání, na kterém padlo polské a maďarské, vetovalo Bulharsko rozhovory o členství se Severní Makedonií. Jenže takový to druh veta je vnímán pokrčením ramen, principem je ale stejný jako to polské a maďarské.

Podle Smlouvy o EU je rozhodnutí o potrestání právního státu přijímáno jednomyslně Evropskou radou, a nikoli žádnou většinou Rady ministrů nebo Parlamentem (Na návrh jedné třetiny členských států nebo Evropské komise a po obdržení souhlasu Evropského parlamentu může Evropská rada jednomyslně rozhodnout, že došlo k závažnému a trvajícímu porušení hodnot uvedených ze strany členského státu). Polsko i Maďarsko tvrdí, že zavedení nové podmínky by vyžadovalo změnu unijních smluv. Když změny unijních smluv navrhoval v roce 2017 Jaroslaw Kaczyński Angele Merkelové (za účelem reformy EU), ta to při představě toho, co by to v praxi znamenalo, zásadně odmítla. Od té doby se s Jaroslawem Kaczyńskim oficiálně nesetkala. Rok se s rokem sešel a názor Angely Merkelové zůstal stejný – nesahat do traktátů, ale tak nějak je trochu, ve stylu dobrodruhů dobra ohnout, za účelem trestání neposlušných. Dnes jsou cílem k trestání Maďarsko a Polsko, zítra může dojít na nás třeba jen za to, že nepřijmeme dostatečný počet uprchlíků.

Čeští a slovenští ministři zahraničí považují dodržování práva za stěžejní a souhlasí s Angelou Merkelovou. Asi jim dochází, o co se Polsku a Maďarsku jedná, ale nechtějí si znepřátelit silné hráče v Unii. Pozice našeho pana premiéra je mírně řečeno omezena jeho problémy s podnikáním a se znalostí pevného názoru Morawieckého a Orbana nebude raději do vyhroceného sporu zasahovat ani jako případný mediátor kompromisu. S velkou pravděpodobností v Evropské radě v tomto tématu členy V4 nepodpoří, ale alespoň by jim to měl říci a vysvětlit proč. Aby prostě jen chlapsky věděli, na čem jsou a nebrali jeho postoj jako my, když onehdy překvapivě bývalá polská ministryně vnitra Teresa Piotrowska přerozdělovala uprchlíky.

Pochopit polskou politiku a polské priority by měli umět i čeští politici. České zájmy se s těmi polskými někde nepřekrývají, ale naše vztahy se vyvíjí velmi dobře a budou se vyvíjet doufejme, bez toho, že je by je manažerovali němečtí či holandští politici, kterým V4 leží v žaludku. Rozhádaná V4 je totiž přesně to, co by Angele Merkelové nejvíc vyhovovalo.

# Morawiecki: Hřbitovy budou na Dušičky uzavřeny

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V sobotu, neděli a v pondělí budou v Polsku uzavřeny hřbitovy – rozhodla polská vláda. Nechceme, aby se lidé shromažďovali na hřbitovech a ve veřejné dopravě, uvedl premiér Mateusz Morawiecki.

„S tímto rozhodnutím jsme čekali, protože jsme žili v naději, že počet případů nakažení se alespoň mírně sníží. Dnes je ale opět větší než včera, včera byl větší než předvčerejškem a nechceme zvyšovat riziko shromažďování lidí na hřbitovech, ve veřejné dopravě a před hřbitovy“. vysvětlil Morawiecki.

Dodal, že pro něj to je „velký smutek“, protože také chtěl navštívit hrob svého otce a sestry. Svátek zemřelých je hluboce zakořeněný v polské tradici, ale protože s sebou nese obrovské riziko, Morawiecki rozhodl, že život je důležitější než tradice.

# Poslankyně opozice atakovaly předsedu PiS

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Ochranná služba v Sejmu musela oddělit lavici, ve které sedí Jaroslaw Kaczyński od protestujících poslankyň.

„Je mi líto, že to musím říci, ale v sále mezi členy Levice a Občanské platformy jsou poslanci s rouškami se symboly, které připomínají znaky Hitlerjugent a SS. Chápu však, že totální opozice odkazuje na totalitní vzorce.“ řekl na začátku zasedání Sejmu místopředseda Sejmu Ryszard Terlecki.

Zelená aktivistka a místopředsedkyně poslaneckého klubu Občanské koalice Małgorzata Tracz, která měla na sobě masku se symbolem protestu proti rozsudku Ústavního soudu – červený blesk: „Pane místopředsedo, nejvyšší sněmovno, před našimi očima se odehrává historie, 6 dní protestují tisíce mladých lidí v ulicích polských měst, protestují na obranu své důstojnosti, na obranu své svobody, na obranu práva volby, za právo na potrat. Toto je válka a tuto válku prohrajete. A kdo je za tuto válku zodpovědný? Pane ministře Kaczyński, to je vaše odpovědnost.“