First slide

Methods of solving first order first degree differential equations

Question

The solution of the differential equation $\sqrt{1 - x^{2}} \sin^{- 1} x d y + y d x = 0$ is

Moderate

A

$y \sec^{- 1} x = c$
B

$y \sin^{- 1} x = c$
C

$x \sin^{- 1} y = c$
D

$x \sec^{- 1} y = c$

Solution

The given equation can be rewritten as $\frac{d x}{\sqrt{1 - x^{2}} \sin^{- 1} x} + \frac{d y}{y} = 0$
$\begin{array}{l} \Rightarrow \int \frac{d x}{\sqrt{1 - x^{2}} \sin^{- 1} x} + \int \frac{d y}{y} = \ln c \\ \Rightarrow \ln |\sin^{- 1} x| + \ln y = \ln c \\ \Rightarrow y \sin^{- 1} x = c \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App