Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Please solve RD Sharma class 12 chapter Differential Equations exercise 21.11 question 17 maths textbook solution

Please solve RD Sharma class 12 chapter Differential Equations exercise 21.11 question 17 maths textbook solution

Answers (1)

best_answer

Answer: proved.

Given: Slope at any point =y+2 x

To find: We have to show that the equation of curve which pass through the origin isy+2(x+1)=2 e^{2 x}

Hint: Use the linear differential equation i.e. \frac{d y}{d x}+P y=Q

Solution: Slope at any point =y+2 x

        \text { i.e. } \frac{d y}{d x}=y+2 x

        =\frac{d y}{d x}-y=2 x

It is a linear differential equation comparing it with \frac{d y}{d c}+P y=Q

        P=-1, Q=2 x

Integrating factor (I f)=e^{\int P d x}

        \begin{aligned} &=>\text { I.F. }=e^{\int(-1) d x} \\\\ &=>\text { I.F. }=e^{-x} \end{aligned}

Solution of the equation is given by

        \begin{aligned} &=y \times \text { I.F. }=\int Q(\text { I.F. }) d x+C \\\\ &=>y e^{-x}=\int(2 x)\left(e^{-x}\right) d x+C \\\\ &=>y e^{-x}=2 \int(x)\left(e^{-x}\right) d x+C \end{aligned}

        =>y e^{-x}=2\left[x \int e^{-x}-\int\left(\frac{d x}{d x} \int e^{-x} d x\right) d x\right]+C[Using integration by parts]

        =>y e^{-x}=2\left(-x e^{-x}+\int 1 e^{-x} d x\right)+C

        =>y e^{-x}=2\left(-x e^{-x}-e^{-x}\right)+C

        \begin{aligned} &=>y e^{-x}=e^{-x}\left(-2 x-2+C e^{x}\right) \\\\ &=>y=-2 x-2+C e^{x} \\\\ &=>y+2(x+1)=C e^{x} \ldots(i) \end{aligned}

If it passes through origin

        \begin{aligned} &=0+2(0+1)=C e^{0} \\\\ &=>C=2 \end{aligned}

Now equation (i) becomes

        =y+2(x+1)=2 e^{x}

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

CBSE Class 10, 12 compartment 2024 exams today for 2.5 lakh students; exam timings, guidelines
anam-khan

CBSE compartment admit card 2024 out at cbse.gov.in; exams from July 15
anam-khan

Reports saying CBSE cannot conduct board exams twice a year currently ‘totally incorrect’; board denies claims

Latest Question