# Non-homogenous heat equation with heat source using variable separation method

I tried to solve using variable separation method. But, i was messed up. Could you please suggest me.

This is a heat equation with heat source $q$.

$m$, $n$, $k$ and $h$ are the constant terms.

The governing equation is

$$mnU_{t}=kU_{xx}+q$$

Initial condition $U(x,0)=T_0$. Boundary conditions

$$U_{x}(0,t)=0$$

$$-kU_{x} (L,t)=h(T(L,t)-T_{0})$$

Thank you.

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What is the nature of $q$? Is it constant, has only $x$ dependence, or $x$ and $t$? Why not combine $m$ and $n$ into a single constant? –  Ron Gordon Feb 9 at 12:52