First slide

Methods of solving first order first degree differential equations

Question

$The solution of the equation \frac{d y}{d x} = \frac{x (2 \log x + 1)}{siny+ycosy} is$

Moderate

A

${ysiny=x}^{2} logx+ \frac{x^{2}}{2} +c$
B

${ycosy=x}^{2} (logx+1) +c$
C

${ycosy=x}^{2} logx+ \frac{x^{2}}{2} +c$
D

${ysiny=x}^{2} logx+c$

Solution

$\int (ycosy+siny) dy= \int (2x lnx+x) dx$
$\int y \cos y d y + \int \sin y d y = 2 \int x \ln x d x + \int x d x$ integrate only first terms
$y \int \cos y d y - \int (1 \int \cos y d y) d y + \int \sin y d y = 2 [\ln x \int x d x - \int (\frac{1}{x} \int x d x) d x] + \int x d x$
$y \sin y - \int \sin y d y + \int \sin y d y = 2 (\ln x \frac{x^{2}}{2} - \int \frac{1}{x} \frac{x^{2}}{2} d x) + \int x d x$
$y \sin y = x^{2} \ln x - \frac{2}{2} \int x d x + \int x d x \Rightarrow y \sin y = x^{2} \ln x + c$

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