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  4. The solution of the equation (dy/dx)=√(1-y2/1-x2) is

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Q. The solution of the equation $\frac{dy}{dx}=\sqrt\frac{1-y^2}{1-x^2}$ is

Differential Equations

Solution:

Given, $\frac{dy}{\sqrt{1-y^{2}}} = \frac{dx}{\sqrt{1-x^{2}}}$
Integrating both sides, we get
$sin^{-1}\, y = sin^{-1}\, x + C$
or $sin^{-1}\, y = sin^{-1}\, x = C$.