Solve nonlinear equation 

$$\left\{\begin{matrix}
-xu\_x+uu\_y=y & \\ 
 u(x,2x)=0& 
\end{matrix}\right.$$

using method of characteristic curves

my attempt:

for the pde we can write it as

$\frac{dx}{-x}=\frac{dy}{u}=\frac{du}{y}$

but i cant solve little please..thank you