I would be thankful to anyone who can present an analytical solution to the following inhomogeneous PDE equation:
$$\frac{\partial{u}}{\partial{t}}= \alpha\frac{\partial^2{u}}{\partial{x^2}}-ku$$
$$u(0,t) = 0$$
$$u(1,t) = M_R$$
$$u(x,0) = x*f(x)$$
where k, $\alpha$ and $M_R$ are constants and k>0.