Answer to Question #215766 in Calculus for smi

Question

Use eigen function expansions to find for value problem. Note: Differential equation must be satisfied 0<x<1, t>0; the pairs of boundary conditions holds for t>0; and the initial conditions holds on 0<x<1.

u_t=u_xx+e^-t , u_x(0, t)=0, u_x(1, t)+u(1, t)=0, u(x, 0)=1-x.