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**Solve BVP by separating variables and using eigenfunction expansion method**

**PDE:U**

_{t}-U_{xx}=e^{-2t}sin(pi x/L)**U=U(x,t)**,x(0,L)

**BC1:U(0,t)=0**

**BC2:U(L,t)=0**

IC:U(x,0)=sin(pi x/L)

U(x,t)=X(x)T(t),X''=(lambda) X ,lambda is the separation of parameter.

I have calculated the basis functions as X

_{n}=root(2/L)sin((n pi x) /L) for n=1,2 and labda

_{n}=-((n pi)/L)

^{2}

Please help to solve the problem