Solve the inhomogeneous heat equation

for $\displaystyle 0<= x <= 1, t >= 0$ with boundary conidtions $\displaystyle z_x (0,t) = 0$ and $\displaystyle z_x (1,t) = 0$

so far i've got

$\displaystyle z = e^-^w^2^t (Acoswx + Bsinwx)$ should be (w^2)t

Is this right first?