A bounded solution to the partial differential equation $\frac{\partial u} {\partial t} = \frac{\partial^2 u} {\partial^2 x} + e^{-t}$.
A. $u(x,t) = e^{-t}$
B. $u(x,t) = e^{-x} e^{-t}$
C. $u(x,t) = e^{-x} + e^{-t}$
D. $u(x,t) = x- e^{-t}$
My Approach:
I found option (d) to be correct by hit and trial of the options mentioned above. Now, my question is how to find the solution with some standard method.