(a) Solve the boundary-value problem 02 u 0x2 5 0u 0t , 0 , x , p, t . 0 u(0, t) 0, u(p

Chapter 13, Problem 11

(choose chapter or problem)

(a) Solve the boundary-value problem

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

u(0, t)=0, \(u(\pi, t)=0\),  t>0

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

(b) What is the solution of the BVP in part (a) if the initial temperature is

\(u(x, 0)=100 \sin 3 x-30 \sin 5 x\)?

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