Get the answer to "Solve the given differential equation by separation of..."

pedzenekO

Answered question

2021-10-13

Solve the given differential equation by separation of variables.

x \sqrt{1 - y^{2}} d x = d y

Alix Ortiz

Skilled2021-10-14Added 109 answers

Given differential equation

x \sqrt{1 - y^{2}} d x = d y

By separating of variables we can write as

\frac{1}{\sqrt{1 - y^{2}}} = x d x

Now integration by using integration property

\int \frac{d y}{\sqrt{1 - y^{2}}} = \sin^{- 1} y

and

\int y^{n} d y = \frac{y^{n + 1}}{n + 1}

\int \frac{1}{\sqrt{1 - y^{2}}} = \int x d x

\sin^{- 1} y = \frac{x^{2}}{2} + c

Which c is integration constant
Result: Solution of differential equation is

\sin^{- 1} y = \frac{x^{2}}{2} + c

Do you have a similar question?

Recalculate according to your conditions!

Didn't find what you were looking for?