Exact Equations & Substitutions · Superchallenge problem

The equation $(x - y)\,dx + (x + y)\,dy = 0$ becomes exact after multiplying by $\dfrac{1}{x^2 + y^2}$. Its solution curve through $(1, 0)$, followed counterclockwise, spirals into the origin. Find the total length of this curve from $(1, 0)$ to the origin.