# The canonical form of a nonlinear second order PDE

Can anyone help me find the canonical form of

$$x^2u_{xy} - yu_{yy} + u_x - 4u = 0?$$

I don't know how to solve it because $a = 0$. I just got that it's hyperbolic since $a=0$ , $b =(x^2)/2$, $c= -y$, then we have $b^2- ac =\frac{x^4}4-0=\frac{x^4}4 > 0$ (hyperbolic), where $x \neq 0$.

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Looks linear to me, with polynomial coefficients. –  Sasha Sep 26 '11 at 19:48