\text{Solve: } xdy+ydx+4\sqrt{(1-x²y²)}dx=0

Answers (1)

Given,

xdy+ydx+4\sqrt{1-x^2y^2}dx=0

xdy+ydx=-4\sqrt{1-x^2y^2}dx

\frac{xdy+ydx}{\sqrt{1-x^2y^2}}=-4dx

As we can see 

\frac{xdy+ydx}{\sqrt{1-x^2y^2}}=sin^{-1}(xy)

So,

d\left (\sin^{-1}(xy) \right )=-4dx

\sin^{-1}(xy) =-4x

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