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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?

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

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  • $\begingroup$ Now I can find the general solution using d'Alambert's solution, awesome. Thanks $\endgroup$
    – MathGuest
    Jan 5, 2014 at 21:16

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