Substitution(Enjoy!)

Calculus Level 5

Given that the solution of the differential equation

xdxydyxdyydx=1y2+x2x2y2 \dfrac{xdx - ydy}{xdy - ydx} = \sqrt{\dfrac{1 - y^{2} + x^{2}}{x^{2} - y^{2}}}

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

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