Characteristics for 2nd order differential formulas

If I have a formula

$p(x)\frac{\partial^2u}{\partial x^2} + r(x)\frac{\partial^2u}{\partial x\partial y} + q(x)\frac{\partial^2 u}{\partial y^2}=f(x,y,u)$

Where $f$ possibly has first partial by-products for $u$.

Can any person offer me a functioned instance of just how to address this making use of the method of features.

Many thanks beforehand.