Limits and DEs

Calculus Level 5

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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