Im giving the pde as follows
$(x+y) \partial _x u+(y-x)\partial_y u=0$.
First I need to show that a continuous solution must be constant and then deduce that the difference of any two continuous solutions to the inhomogenous pde
$ (x+y) \partial _x u+(y-x)\partial_y u=f(x.y)$ $
only differ by a constant. And last find the unique solution to the pde with f(x,y)=y and ivc $u(0,0)=0$.
First I tried to find the characteristic curves by solving $ \frac{dy}{dx}=\frac{y-x}{x+y}$. But I cant solves this ode hence I cant really get anywhere with this exercise.
Any help?
