Khaleesi Herbert

2020-11-08

Solve differential equation$x{y}^{\prime}=(1-{y}^{2}{)}^{\frac{1}{2}}$

lamanocornudaW

Skilled2020-11-09Added 85 answers

The given differential equation is $\sqrt{1-{y}^{2}}$

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

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

Integrating both sides, we obtain

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

$\Rightarrow si{n}^{-1}(y)=ln(|x|)+c$

$\Rightarrow y=\mathrm{sin}(ln(|x|)+c)$

Integrating both sides, we obtain

Jeffrey Jordon

Expert2021-10-23Added 2575 answers

Answer is given below (on video)

Jeffrey Jordon

Expert2021-12-14Added 2575 answers

Answer is given below (on video)