hi sorry for the insurgent of questions ..
anyways we have :
du/dx + x*du/dy = 0
with boundary conditions
i) u = sinh(y) on x=0
ii) u = cosh(x) on y=0
question: solve pde above and show solution is single valued throughout (x,y) plane.
heres what i have so far:
I get 2 integrals I = u and J = y-(x^2)/2 so general solution to pde is
u = f(y-(x^2)/2)
but not sure where to go from here : /