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

Chapter 10, Problem 6E

(choose chapter or problem)

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

$\frac{\partial u}{\partial t}=7 \frac{\partial^{2} u}{\partial x^{2}}, \quad 0<x<\pi, \quad t>0$,

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

$u(x, 0)=1-\sin x, \quad 0<x<\pi$,

Equation Transcription:

$\frac{\partial{}u}{\partial{}t}=7\frac{{\partial{}}^{2}u}{\partial{}{x}^{2}},\ 0<x<\pi{},\ \ \ t>0$

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

$u(x,0)=1-sin\ x,\ \ \ 0<x<\pi{}$

Text Transcription:

partial u/partial t=7 partial^2 u/partial x^2, 0<x<pi, t>0

partial u/partial x(0,t)=partial u/partial x(pi,t)=0, t>0

u(x,0)=1-sin x, 0<x<pi

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