Separation of variables

Submitted by vic777 on Sat, 10/27/2007 - 06:09.

What would be the solution for:
$u_t_t-4u_x_x=0, 0<x<1, t>0,$
$u(x,0)=\sin\frac{\pi x}{2}, u_t(x,0)=1+x, 0\le x\le1,$
$u(0,t)=0,u_x(1,t)=0, t\ge0$