In 1–10, find a formal solution to the given initial-

Chapter 10, Problem 1E

(choose chapter or problem)

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

$\frac{\partial u}{\partial t}=5 \frac{\partial^{2} u}{\partial x^{2}}, 0<x<1, t>0$

$u(0, t)=u(1, t)=0, t>0$

$u(x, 0)=(1-x) x^{2}, 0<x<1$

Equation Transcription:

$\frac{\partial{}u}{\partial{}t}=5\frac{{\partial{}}^{2}u}{\partial{}{x}^{2}},\ 0<x<1,\ t>0$

$u(0,t)=u(1,t)=0,\ t>0,$

$u(x,0)=(1-x){x}^{2},\ 0<x<1$

Text Transcription:

\partial u\partial t=5 \partial^2 u\partial x^2, 0<x<1, t>0

u(0, t)=u(1, t)=0, t>0

u(x, 0)=(1-x) x^{2}, 0<x<1

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