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**<< Mentor Note -- thread moved from the technical math forums >>**

I am getting stuck on this partial differential equation.

U

_{t}= U

_{xx}- U + x ; 0<x<1

U(0,t) = 0

U(1,t) = 1

U(x,0) = 0

Here is my work so far :

U = e

^{-t}w + x

gives the new eq w

_{t}=w

_{xx}

to get rid of boundary conditions :

w=x+W

W

_{t}=W

_{xx}

W(0,t) = 0

W(1,t)=0

W(x,0)=-x

W=X(x)T(t)

Plug that in, and I get these :

T'=μT

X''=μx

w = e

^{-(nπ)2t}[a

_{n}sin(nπx)]

a

_{n}= -2∫xsin(nπx) = 2cos(nπ)/nπ

w = x + W

w = x +(2/π)Σ(1/n)cos(nπ)sin(nπx)e

^{-(nπ)2t}

u = e

^{-t}w + x

u = x + e

^{-t}(x +(2/π)Σ(1/n)cos(nπ)sin(nπx)e

^{-(nπ)2t})

But the books answer is :

u(x,t) = x - (2/π)e

^{-t}* [ e

^{-π2t}sin(πx) - (1/2) e

^{-2π2t}sin(2πx)+...]

What am I doing wrong?

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