Is this non-homogeneous partial differential equation analytically solvable and if not what would be an appropriate numerical method?

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The equation is:

$$\frac{\partial h}{\partial t} = \frac{\nu}{(Ft)^2}\frac{\partial^2 h}{\partial \theta^2} + \eta(\theta,t)$$

where $\nu$ and $F$ are constants and $\eta$ is a function of $\theta$ and $t$. The equation is subject to periodic BCs in $\theta$, $\theta \in [0,2\pi)$, and $h(\theta,0) = 0$.

If it is solvable could you please provide a hint to the right direction to solve it? If not what would be an appropriate numerical method? Many thanks.