Differential Equations · Superchallenge problem

A solution curve of $\dfrac{dy}{dx}=\dfrac{x+y}{x-y}$ passes through $(1,0)$. Using the substitution $y=vx$ (or polar coordinates), the curve can be written with $\arctan\!\left(\dfrac{y}{x}\right)=\dfrac12\ln(x^2+y^2)$. Find $x^2+y^2$ at the point where this curve crosses the line $y=x$.