Exact Equations & Substitutions · Superchallenge problem

Consider $y' = \dfrac{y^2 - x^2}{2xy}$. Let $y_1$ be its solution with $y_1(1) = 1$ and $y_2$ its solution with $y_2(1) = 3$, each continued as far as it goes (with $x > 0$, $y > 0$). Find the area of the region above the $x$-axis lying under the graph of $y_2$ but not under the graph of $y_1$.