Solving a Stochastic PDE with two variables in time

Question

I am trying to work on exercise 5.13 in the book Arbitrage Theory in Continuous time by Thomas Bjork. The equation to solve is; \begin{eqnarray*} \frac{\partial F}{\partial t} (t,x,y) + \frac{1}{2} \sigma^2 \frac{\partial^2 F}{\partial x^2} (t,x,y) + \frac{1}{2} \delta^2 \frac{\partial^2 F}{\partial y^2} (t,x,y) &= 0\\ F(T,x,y) &= xy\end{eqnarray*} I seem not to see how I can start off, especially due to the fact that I am used to solving when the equation has only one variable in time. How can I go about this when they are now two variables in time? Thanks a lot.