First slide

Methods of solving first order first degree differential equations

Question

$The general solution of the differential equation \frac{d y}{d x} + \sin \frac{(x + y)}{2} = \sin \frac{(x - y)}{2} is$

Moderate

A

$logtan(y/2)=C-2sinx$
B

$log tan(y/4)=C-2sin(x/2)$
C

$logtan (\frac{y}{4} + \frac{π}{4}) =C-2sin(x/2)$
D

$logtan (\frac{y}{2} + \frac{π}{4}) =C-2sinx$

Solution

$\begin{array}{l} \frac{d y}{d x} = \sin (\frac{x}{2} - \frac{y}{2}) - \sin (\frac{x}{2} + \frac{y}{2}) \\ \frac{d y}{d x} = - 2 \cos \frac{x}{2} \sin \frac{y}{2} \\ \frac{1}{2} \frac{d y}{\sin \frac{y}{2}} = - \cos \frac{x}{2} d x \\ \frac{1}{2} \int cosec \frac{y}{2} d y = - \int \cos \frac{x}{2} d x \\ \Rightarrow \ln (\tan \frac{y}{4}) = \frac{- \sin \frac{x}{2}}{\frac{1}{2}} + C \\ \Rightarrow \ln (\tan \frac{y}{4}) = C - 2 \sin \frac{x}{2} \end{array}$

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