# Solve differential equation xy'=(1-y^2)^{frac{1}{2}}

Solve differential equation$x{y}^{\prime }=\left(1-{y}^{2}{\right)}^{\frac{1}{2}}$
You can still ask an expert for help

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

lamanocornudaW
The given differential equation is $\sqrt{1-{y}^{2}}$
$⇒x\frac{dy}{dx}=\sqrt{1-{y}^{2}}$
$⇒\frac{1}{\sqrt{1-{y}^{2}}}dy=\frac{dx}{x}$
Integrating both sides, we obtain
$\int \frac{1}{\sqrt{1-{y}^{2}}}dy=\int \frac{dx}{x}$
$⇒si{n}^{-1}\left(y\right)=ln\left(|x|\right)+c$
$⇒y=\mathrm{sin}\left(ln\left(|x|\right)+c\right)$

Jeffrey Jordon

Answer is given below (on video)

Jeffrey Jordon

Answer is given below (on video)