Find an explicit solution $\displaystyle u(x, y)$ which satisfies
$\displaystyle xu_x +u_y = \frac{1}{u}$ with $\displaystyle u(1,y) =y$
Find the Jacobian of the transformation you use to reduce the PDE to an ODE.
See if you can follow post #2 in this thread.
http://www.mathhelpforum.com/math-he...ty-153048.html