Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa

Solution of diff eqn x(y^{2}+y)dx+\left ( x+1 \right )dy=0^{} is

  • Option 1)

    (y+1)(x+1)=c

  • Option 2)

    (y+1)(x+1)=cx^{2}

  • Option 3)

    (y+1)(x+1)=ce^{x}

  • Option 4)

    None of these

 

Answers (1)

best_answer

As we learnt

 

Variable Separation Method -

 

integrating, we get

\int f\left ( x \right )dx+\int \phi \left ( y \right )dy =c

-

 

 

\Rightarrow xy\left ( y+1 \right )dx+\left ( x+1 \right )dy= 0

Dividing throughout by y(y+1)(x+1) we get

\frac{xdx}{\left ( x+1 \right )}+\frac{dy}{y\left ( y+1 \right )}= 0

\Rightarrow \int \frac{xdx}{\left ( x+1 \right )}+\int \frac{dy}{y\left ( y+1 \right )}= c

\Rightarrow \int \frac{(x+1)-1}{\left ( x+1 \right )}dx+\int \frac{(1+y)-y}{y\left ( y+1 \right )}dy= c

\Rightarrow \int \left ( 1-\frac{1}{\left ( x+1 \right )} \right )dx+\int \left ( \frac{1}{y}-\frac{1}{y+1} \right )dy= c

\Rightarrow x-\ln\left | x+1 \right |+\ln\left | y \right |-\ln\left | y+1 \right |= c

\Rightarrow \ln\left | \frac{y}{\left ( x+1 \right )\left ( y+1 \right )} \right |= c-x

\Rightarrow \left | \frac{y}{\left ( x+1 \right )\left ( y+1 \right )} \right |= e^{c-x}= \Rightarrow \left | \frac{y}{\left ( x+1 \right )\left ( y+1 \right )} \right |= c.e^{-x}

 


Option 1)

(y+1)(x+1)=c

Option 2)

(y+1)(x+1)=cx^{2}

Option 3)

(y+1)(x+1)=ce^{x}

Option 4)

None of these

Posted by

Himanshu

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

JEE Main 2026: IIT Roorkee’s ECE emerges as top choice after CSE; closing rank rises
anam-khan

JEE Main 2026 application correction begins on jeemain.nta.nic.in; edit details by December 2
anam-khan

JEE Mains 2026 LIVE: NTA to conduct session 1 from January 21 to 30; exam pattern, syllabus

Latest Question