Dear users of MHF, I've found two PDE question very challenging, would you guys mind to give some hints?

First question:

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.

second question:

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...