# Characteristics for 2nd order differential equations

If I have an equation

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

Where $f$ maybe contains first partial derivatives for $u$.

Can anyone give me a worked example of how to solve this using the method of characteristics.

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See these lecture notes on the method of characteristics for second-order PDEs, where the method is applied to steady isentropic flow (gasdynamics)

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