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 18

Provide solution for RD Sharma maths class 12 chapter Differential Equations exercise 21.11 question 18

Answers (1)

best_answer

Answer: y e^{-3 x}=\left(-\frac{2}{3} x-\frac{2}{9}\right) e^{-3 x}+\frac{26}{9} e^{-3}

Given: Tangent makes an angle (2 x+3 y) with x-axis

To find: We have to show that the equation of curve which pass through (1,2)

Hint: Find the slope of the tangent then solve using linear differential equation.

Solution: Slope of tangent t=\tan \theta and tangent makes angle (2 x+3 y)

        =>\frac{d y}{d x}=\tan \left[\tan ^{-1}(2 x+3 y)\right]

        =>\frac{d y}{d x}=2 x+3 y

        =>\frac{d y}{d x}-3 y=2 x

It is a linear differential equation

Comparing it with  \frac{d y}{d x}+P y=Q

        =P=-3, Q=2 x

        \begin{aligned} &\text { If }=e^{\int P d x} \\\\ &=>I f=e^{-\int 3 d x} \\\\ &=>I f=e^{-3 x} \end{aligned}

Solution of equation is given by

        =y(I f)=\int Q(I f) d x+C \\

        =>y\left(e^{-3 x}\right)=\int 2 x e^{-3 x} d x+C

Using integration by parts we get

        \begin{aligned} &=>y\left(e^{-3 x}\right)=2\left[x \int e^{-3 x}-\int\left(\frac{d x}{d x} \int e^{-3 x} d x\right) d x\right]+C \\\\ &=>y\left(e^{-3 x}\right)=2\left[-\frac{x e^{-3 x}}{3}-\frac{1}{3} \int e^{-3 x} d x\right]+C \end{aligned}

        \begin{aligned} &=>y\left(e^{-3 x}\right)=-\frac{2}{3} x e^{-3 x}-\frac{2}{3} e^{-3 x} \times \frac{1}{3}+C \\\\ &=>y\left(e^{-3 x}\right)=-\frac{2}{3} x e^{-3 x}-\frac{2}{9} e^{-3 x}+C \end{aligned}

Taking e^{-3 x} common on both sides

        =>y=-\frac{2}{3} x-\frac{2}{9}+C \ldots(i)

If it passes through \left ( 1,2 \right )

        \begin{aligned} &=>2=-\frac{2}{3} \times 1-\frac{2}{3}+C e^{3} \\\\ &=>C=\frac{26}{9} e^{-3} \end{aligned}

So equation (i) becomes

        =>y e^{-3 x}=\left(-\frac{2}{3} x-\frac{2}{9}\right) e^{-3 x}+\frac{26}{9} e^{-3}

 

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