I was trying to solve the following problem:
The integral surface of the pde $xu_x+yu_y=0$ satisfying the condition $u(1,y)=y$ is given by:
I was trying to apply Lagrange's method but i could not get the desired result. I see that option $(a)$ satisfies the given equation and so $(a)$ should be the right choice. But i could not get it directly. Please help.Thanks in advance for your time.