In these exercises, do not make a reduction to homogeneous boundary conditions. Solve the initial value problem for the heat equation with time-dependent sources

∂u/∂t​=k ∂²u​/∂x²+Q(x,t)
u(x,0)​=f(x)
subject to the following boundary conditions:

∂u​/∂x (0,t)=A(t), ∂u/∂x​(L,t)=B(t)