I'm having trouble in solving a specific partial differential equation. It writes: $$ \dfrac{\partial p}{\partial t} = c \left( \dfrac{\partial^{2} p}{\partial x_{1}^{2}} + \cos^2\left(\theta\right) \dfrac{\partial^{2} p}{\partial x_{2}^{2}} + \sin^2\left(\theta\right) \dfrac{\partial^{2} p}{\partial x_{3}^{2}} - 2\sin(\theta)\cos(\theta) \dfrac{\partial^{2} p}{\partial x_{2} \partial x_{3}} \right), $$ where $p$ is a function of $x_1,x_2,x_3,t$ and $\theta$, and $c$ is constant. The known boundary conditions are: $$ p(x_3=0) = 0, \\ \dfrac{\partial p(x_3 = h)}{\partial x_3} = 0, $$ and the initial condition is: $$ p(t=0) = d \mbox{, with } d \mbox{ being constant.} $$ I'm certainly a bit rusty in solving PDEs, and after some trials, I don't see a clue.
Until now I've tried by taking the double Fourier transform in $x_1$ and $x_2$, and next, taking the Laplace transform of that. I can solve, in that space, for $x_3$. But the way back to $x_1$, $x_2$ and $t$ results in a too complicated and perhaps not possible path.
I'd really appreciate if someone takes the time, knowledge, and effort to give me a hint, even if the hint is an impossibility.
Thank you all!