need solution

First Order Cauchy Problem Problem 4 (a) Solve the PDE Tur - yuy + (x' +y? )u = x2 -y? on U = {(x, y) ER' : x, y > 0}. "Solve" here means "Find all possible C' solutions." Your solution should de- pend on an arbitrary function which you will need to introduce. Knowing how to do that is part of the problem. (This is like if someone says: Solve a" = 0. Then you know x = at + b with two arbitrary constants a and b.) Hint(s): Consider the characteristic field v = (x, -y) on the first quadrant U. Plot it with numerical software if necessary. Choose an appropriate non- characteristic curve. (b) Solve the Cauchy problem: Tium + 2xzur + Urg = 3u u(11, 12, 0) = 9(21, 12). 4