In 17–19, find the solution to the heat flow problem.

Chapter 10, Problem 18E

(choose chapter or problem)

In Problems 17-19, find the solution to the heat flow problem.

$\frac{\partial u}{\partial t}=5 \frac{\partial^{2} u}{\partial x^{2}}, \quad 0<x<\pi, \quad t>0 $

$u(0, t)=u(\pi, t)=0, t>0$,

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

where $f(x)$ is given.

$f(x)=x(\pi-x)$

Equation Transcription:

$\frac{\partial{}u}{\partial{}t}=5\frac{{\partial{}}^{2}u}{\partial{}{x}^{2}},\ \ 0<x<\pi{},\ \ t>0$

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

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

$f(x)$

$f(x)=x(\pi{}-x)$

Text Transcription:

\partial u \partial t=5 \partial^2 u\partial x^2, \quad 0<x<\pi, \quad t>0

u(0, t)=u(\pi, t)=0, t>0

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

f(x)

f(x)=x(\pi-x)

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