Solved: In 1–10, find a formal solution to the given

Chapter 10, Problem 5E

(choose chapter or problem)

In Problems 1-10, find a formal solution to the given initial-boundary value problem.

$\frac{\partial u}{\partial t}=\frac{\partial^{2} u}{\partial x^{2}}, 0<x<\pi, t>0$

$\frac{\partial u}{\partial x}(0, t)=\frac{\partial u}{\partial x}(\pi, t)=0, t>0$

$u(x, 0)=e^{x}, 0<x<\pi$

Equation Transcription:

$\frac{\partial{}u}{\partial{}t}=\frac{{\partial{}}^{2}u}{\partial{}{x}^{2}},\ 0<x<\pi{},\ t>0$

$\frac{\partial{}u}{\partial{}x}(0,t)=\frac{\partial{}u}{\partial{}x}(\pi{},t)=0,\ t>0,$

$u(x,0)={e}^{x},\ 0<x<\pi{}$

Text Transcription:

\partial u}{\partial t}=\frac{\partial^{2} u}{\partial x^{2}}, 0<x<\pi, t>0

\partial u}{\partial x}(0, t)=\frac{\partial u}{\partial x(\pi, t)=0, t>0

u(x, 0)=e^{x}, 0<x<\pi

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