The homogeneous part of the solution is easy
I have a idea but not sure if it is correct.
non-homogeneous part of the solution of $a(x,y)u_x+b(x,y)u_y=f(x,y)$ is:$\int_C f(x,y/(a^2+b^2)ds$
where the integral is along the characteristic curve C
I do not know if it is correct.
Also can some one guide me to show $(1/x)u_x+(1/y)u_y=1/y$ subject to $u(x,1)=(3-x^2)/2$