Hey guys. I'm working on the IVP

$\displaystyle u_y=xuu_x$, $\displaystyle u(x,0)=x$,

andgiventhe implicit solution $\displaystyle x=ue^{-yu}$.

(This is from Fritz John's Partial Differential Equations, 4th Ed, exercise 1.6.1b p18.)

It's easy to show that this is indeed a solution, but now I am expected (I think) to put it into explicit terms, i.e. in the form $\displaystyle u=u(x,y)$. (This is the reason this is in the analysis section.)

Any help would be much appreciated. Thanks!