# Limits and DEs

Calculus Level 4

If $$\displaystyle \frac {dy}{dx} = - \frac {x(1+y^{2})^{2}}{\ln y (1-y^{2})}$$, $$y(1)=1$$ and $$\displaystyle \lim_{y \to \infty} x(y) = \sqrt{\frac {A \pi}{B} + C}$$, where $$A$$ and $$B$$ are coprime positive integers, find the value of $$A + B + C$$.

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