Question

Find the solution of the differential equation $\frac{dy}{dx}=\frac{\sqrt{1-y^2}}{y}$.

Answer 1

Given, the differential equation,

$\frac{dy}{dx}=\frac{\sqrt{1-y^2}}{y}$

or, $-\frac{1}{2}\frac{-2y}{\sqrt{1-y^2}}dy=dx$

Integrating we have,

$-\frac{1}{2}.2.\sqrt{1-y^2}=x+c$

or, $-\sqrt{1-y^2}=x+c$ [ Where $c$ being integrating constant]