Question

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

Answer 1

$x + \sqrt{1-y^2} = C$

Answer 2

The given differential equation is separable. Separate variables $y$ and $x$ to opposite sides of the equation. Integrate $\int \frac{y}{\sqrt{1-y^2}} dy$ using substitution $u=1-y^2$, which yields $-\sqrt{1-y^2}$. Integrate $\int dx$ which yields $x$. Equate the results and combine constants to get the general solution $x + \sqrt{1-y^2} = C$.