# Solution of a particular PDE in 4 variables with non-constant coefficients

I have come across the following equation while reading about the Unruh Effect in Black Hole Physics. . K is a function of $x,y,\rho,t$ i.e $K=K(x,y,\tau, \rho)$. $\omega, k,m$ are constants. $$\rho^2 \frac{\partial^2 K}{\partial \rho^2}+\omega^2 \frac{\partial^2K}{\partial \tau ^2}-k^2 \rho^2 (\frac{\partial^2 K}{\partial x^2}+\frac{\partial^2K}{\partial y^2})-\rho^2m^2K=0$$

How do I solve it?

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Perhaps there is a suitable change of variable(s) that will simplify the equation? I think $P = \ln \rho$ may be a good place to start but I'm not sure where to go from there. –  in_wolfram_we_trust Jul 1 '13 at 13:26
On closer consideration, that only makes the first term simpler. The rest get a lot messier. –  in_wolfram_we_trust Jul 1 '13 at 13:27