Explained: "Solve differential equationxy′=(1−y2)12"

Name: Solve differential equationxy′=(1−y2)12
Uploaded: 2022-02-23T17:22:57+00:00
Description: Solve differential equationxy′=(1−y2)12

Khaleesi Herbert

Answered question

2020-11-08

Solve differential equation

x y^{'} = (1 - y^{2})^{\frac{1}{2}}

Answer & Explanation

lamanocornudaW

Skilled2020-11-09Added 85 answers

The given differential equation is

\sqrt{1 - y^{2}}

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

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

Integrating both sides, we obtain

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

\Rightarrow s i n^{- 1} (y) = l n (| x |) + c

\Rightarrow y = \sin (l n (| x |) + c)

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)

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