I need b part of this pde question handwritten and correctly 4. The one dimensional wave equation describes how waves of speed c propogate along ataught string. It is given by the formulaƏt2u(x, t) = c²-da2 u(x, t).This is a partial differential equation. In MATH , we’ve only learned how tosolve ordinary differential equations. However, using the multivariable chain rule,we’ll show that this problem is indeed tractablea) By introducing variablesn= x – ct, a = x + ct,show that the wave equation becomesda= 0n-b) Show that u =F(a) + G(n) is a solution for any two functions F and G.

Answered: Image /qna-images/answer/2e735a48-65c4-40c7-95ba-94d4d2d91674.jpg

The one dimensional wave equation describes how waves of speed c propogate along a taught string. It is given by the formula dt? "(x, t) = c²- car2 u (x, t). This is a partial differential equation. In MATHE, we’ve only learned how to solve ordinary differential equations. However, using the multivariable chain rule, we'll show that this problem is indeed tractable a) By introducing variables n = x – ct, a = x + ct, show that the wave equation becomes da b) Show that u = F(a) + G(n) is a solution for any two functions F and G. %3D

The one dimensional wave equation describes how waves of speed c propogate along a taught string. It is given by the formula dt? "(x, t) = c²- car2 u (x, t). This is a partial differential equation. In MATHE, we’ve only learned how to solve ordinary differential equations. However, using the multivariable chain rule, we'll show that this problem is indeed tractable a) By introducing variables n = x – ct, a = x + ct, show that the wave equation becomes da b) Show that u = F(a) + G(n) is a solution for any two functions F and G. %3D

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter11: Differential Equations

Section11.1: Solutions Of Elementary And Separable Differential Equations

Problem 59E: According to the solution in Exercise 58 of the differential equation for Newtons law of cooling,...

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