
11.5.3.7 With variable coefficients
Problem:
Bring the following equation to the canonical form in each of the regions, where the type of the considered equation is preserved:
\[
x^{2} u_{x x}+2 x y u_{x y}+y^{2} u_{y y}-2 y u_{x}+y e^{\frac{y}{x}}=0 .
\]