Hello

I have one problem with solve heat equation with integral Fourier,

This is problem

du/dt-d(2)u/dx^2= 2t when 0<x<$\displaystyle \pi $, 1 when x>0

u(x,0)=2x when o<x<1 , -1 when x>1

u(0,t)=t-1 when t$\displaystyle \geqslant $0

I write u(x,t)=F(x)G(t) and try to find answer!

but I can not find a(w) and b(w) and also G(t)