If $x \in (-\infty, \infty)$ & $y \in (-1,1)$ , then $x^2 \frac{\partial^2u}{\partial x^2}+(1-y^2)\frac{\partial^2u}{\partial y^2}=0$ represents?

Question

For $-\infty<x< \infty$ and $-1<y<1$,the partial differential equation $$x^2 \frac{\partial^2u}{\partial x^2}+(1-y^2)\frac{\partial^2u}{\partial y^2}=0$$ represents _____?

My Approach:
We know general form of $2nd$ order differential eq. is: $$Au_{xx}+2Hu_{xy}+Bu_{yy}+2Gu_x+2Fu_y+Cu=K$$ if $H^2=AB$ ,then it represents parabola
if $H^2<AB$ ,then it represents ellipse
& if $H^2>AB$ ,then it represents hyperbola
In this problem:
$A=x^2$ & $B=(1-y^2)$ ;also $x \in (-\infty, \infty)$ & $y \in (-1,1)$
then how can we interprets its curve?
please help...