Dear users of MHF, I've found two PDE question very challenging, would you guys mind to give some hints?
1) (-x) Ux + (2y) Uy = x^2 + y^2
a) find the characteristic curve (I solved)
b) solve the above equation by conditions U(x,1)= x^2 , u(x,-1) = x.
2)Ux + Uy= x - y + U
condition : U(0,y)= e^(-y^2).
for the second question I tried U = x^2 - (xy) + f(x-y) e^(x)
but I yielded a result like x - y + f(x-y)e^(x)....
the questions just sound so impossible for me...
and the condition in 1b was so tricky...