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

#### Solution

Given, the differential equation,
$\dfrac{dy}{dx} = \dfrac{\sqrt{1 - y^2}}{y}$
or, $-\dfrac{1}{2}\dfrac{-2y}{\sqrt{1-y^2}}dy=dx$
Integrating we have,
$-\dfrac{1}{2}.2.\sqrt{1-y^2}=x+c$
or, $-\sqrt{1-y^2}=x+c$ [ Where $c$ being integrating constant]