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]