General solution of a second order PDE

Question

I have the second order PDE
$t^5u_{xx}-tu_{tt}+2u_t=0$
and need to find it's general solution. My problem is that since it's a second order PDE the method for first order quasi-linear PDE doesn't seem to work and the variable separation method won't help either since I need a general solution.
So, what would be the correct procedure to solving this?

Answer 1

Hint: look for a change of variables $t = T^p$. For a suitable $p$, you'll get the wave equation in $x$ and $T$.