Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Provide solution for RD Sharma maths class 12 chapter Differential Equations exercise 21.11 question 14

Provide solution for RD Sharma maths class 12 chapter Differential Equations exercise 21.11 question 14

Answers (1)

Answer: 2 x y-2 x-y-2=0

Given: The differential equation is y-x \frac{d y}{d x}=y^{2}+\frac{d y}{d x} .

To find: We have to find the equation of the curve which passes through \left ( 2,2 \right )

Hint: We will integrate the given differential equation and then we use the points \left ( 2,2 \right )

Solution: we have,

        =y-x \frac{d y}{d x}=y^{2}+\frac{d y}{d x}

Integrating on both sides we get,

        \begin{aligned} &=>\int\left(y-x \frac{d y}{d x}\right)=\int\left(y^{2}+\frac{d y}{d x}\right) \\\\ &=>\int \frac{d y}{y-y^{2}}=\int \frac{d x}{1+x} \end{aligned}

        \begin{aligned} &=>\int \frac{d y}{y(1-y)}=\int \frac{d x}{1+x} \\\\ &=>\int\left[\frac{1}{y}-\frac{1}{1-y}\right] d y=\int \frac{d x}{x+1} \end{aligned}

        =>\log |y|-\log |1-y|=\log |x+1|+C \ldots(i)

Since the curve passing through the point \left ( 2,2 \right ) it satisfies equation (i)

Then,

        \begin{aligned} &\log |2|-\log |1-2|=\log |2+1|+C \\\\ &\log |2|-\log |-1|=\log |3|+C \\\\ &C=\log |2|-\log |3| \\\\ &C=\log \left|-\frac{2}{3}\right| \end{aligned}

Putting the value of C in equation (i) we get

        \begin{aligned} &\log |y|-\log |1-y|=\log |x+1|+\log \left|-\frac{2}{3}\right| \\\\ &\log \left|\frac{y}{1-y}\right|=\log \left|-\frac{2(x+1)}{3}\right| \end{aligned}

Taking antilogarithm on both sides,

        \begin{aligned} &\frac{y}{1-y}=-\frac{2(x+1)}{3} \\\\ &3 y=-2(x+1)(1-y) \\\\ &3 y=-2(1+x-y-x y) \\\\ &3 y=-2-2 x+2 y+2 x y \end{aligned}

        \begin{aligned} &3 y+2+2 x-2 y-2 x y=0 \\\\ &y+2+2 x-2 x y=0 \\\\ &2 x y-2 x-2-y=0 \end{aligned}

Hence, required equation is found.

Posted by

infoexpert26

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

Board Exam Time Table 2025 Live: UP Board exams from February 24; CBSE, BSEB date sheet soon
anam-khan

CBSE Date Sheet 2025 Live: Class 10, 12 board exam dates soon; syllabus, sample papers
anam-khan

Extra time in CBSE exams for students with type 1 diabetes: Kerala SHRC seeks report on plea

Latest Question