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## Homework Statement

Find a formal solution to the given initial boundary value problem.

du/dt=5(d^2u/dx^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

## Homework Equations

1) u(x,t) = a

_{0}/2 + sum[a

_{n}*e^(-b(n pi/L)^2*t) * cos(n pi x/L)

2) Fourier series equation

## The Attempt at a Solution

(1-x)(x^2) = a

_{0}/2 + sum(a

_{n}* cos(n pi x) with c

_{n}= a

_{n}

I calculate a

_{0}=1/6

a

_{n}= 2* integral[(1-x)(x^2)(cos n pi x)dx] from 0 to 1

I'm wondering if this is write so far? And if so, how do I proceed from here? Do I just plug everything back into the general u(x,t) equation?

Thanks!