Substitution(Enjoy!)

Calculus Level 5

Given that the solution of the differential equation

\[ \dfrac{xdx - ydy}{xdy - ydx} = \sqrt{\dfrac{1 - y^{2} + x^{2}}{x^{2} - y^{2}}}\]

is \( \sqrt{f(x , y)} + \sqrt{1 + f(x , y)} = c\left ( \dfrac{x + y}{\sqrt{f(x , y)}} \right ),\) with \(c\) an arbitrary constant, find \(60f(3 , 2)\).

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