Ou let a, b e r be such that a2 + b2 # 0. then the cauchy problem a - ba =1 u(x, y) = x on ox ax + by= 1 (a) has more than one solution if either a or b is zero

I have attached my attempt for this problem. My question is, how do I determine the uniqueness of the solution from the condition obtained (please see the attached pic)