11.5.3.3 With variable coefficients

Problem: Find the solution of the second order linear equation, satisfying the given initial conditions: \[ \begin{array}{l} u_{x y}-\frac{1}{y^{2}+1} u_{x}=0, \quad y>0, \quad x>0 . \\ \left.u\right|_{x=0}=y,\left.\quad u\right|_{y=0}=x . \end{array} \]