Exact Equations & Substitutions · Challenge problem

The solution of $y' = \dfrac{y}{x} - \dfrac{x^2}{y}$ with $y(1) = 1$ is positive on an interval $0 < x < b$ and reaches $0$ as $x \to b$. Find the area of the region between the graph of this solution and the $x$-axis for $0 < x < b$.