Did you obtain tbe general solutions
In (2) you mentioned you tried Where did this come from?
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...
for 2) I only know that or usually results in , how ever the x-y parts I find it so hard...
if i let ,
but then applying the condtion given I can't get the answer
For the first part, subs into your solution, set this equation the the IC and solve for . For example,
Let so . This then defines . Similarly for the second IC.
For the second question, do you know the method of characteristics?