Hello, I'm having difficulty finding the Cn for a heat conduction problem, and any help would be appreciated.

The problem is #8, Section 10.5 in Boyce and DiPrima if you have it.

Uxx = 4Ut, 0 < x < 2, t>0

U(0,t) = 0 = U(2,t), t>0

U(x,0) = 2sin(pi x / 2) - sin(pi x) + 4sin(2pi x)

Thanks.