PDE question.

Hi,

1. The problem statement, all variables and given/known data

I have solved u_x + (x/y)u_y = 0 using characteristics, to obtain

u(x,y)=C (for y=+-x) and f(x²-y²)





2. Relevant equations







3. The attempt at a solution

I was then given two boundary conditions:

(a) u(x=0,y)=cos(y), which I used to obtain u(x,y) = cos(√(y²-x²))

(b) u(x=y,y)=y

I am not quite sure how to approach this latter and would appreciate some advice.