Find a formal solution to the initial-boundary value

Chapter 10, Problem 12E

(choose chapter or problem)

Find a formal solution to the initial-boundary value problem

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

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

$t>0$,

$u(x, 0)=f(x), 0<x<\pi$

Equation Transcription:

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

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

$t>0$

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

Text Transcription:

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

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

t>0

u(x, 0)=f(x), 0<x<\pi

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