Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Please Solve R.D.Sharma class 12 Chapter 21 Differential Equations Exercise 21.8 Question 4 Maths textbook Solution.

Please Solve R.D.Sharma class 12 Chapter 21  Differential Equations Exercise 21.8 Question 4 Maths textbook Solution.

Answers (1)

Answer:-    x+y=\tan \left ( x+c \right )

Given:\frac{dy}{dx}=\left ( x+y \right )^{2}

Hint : - Differential equation of the form \frac{dy}{dx}=\int \left ( ax+by+c \right )can be reduced to variable separable form by substitution ax+by+c=v

Solution : -  We have,

                     \frac{dy}{dx}=\left ( x+y \right )^{2}

Let x+y=v

Differentiating with respect to x, we get,

                            \begin{aligned} \; \; \; \; \; \; &\quad \frac{d }{d x}(\mathrm{x}+\mathrm{y})=\frac{d}{d x}(v) \\ &\Rightarrow \quad 1+\frac{d y}{d x}=\frac{d v}{d x} \\ &\Rightarrow \frac{d y}{d x}=\frac{d v}{d x}-1 \end{aligned}

Putting the value of \frac{dy}{dx} in equation (i), we get

\frac{d v}{d x}-1=(\mathrm{x}+\mathrm{y})^{2} \\

\Rightarrow \frac{d v}{d x}-1=\mathrm{v}^{2}                                            (\because \mathrm{x}+\mathrm{y}=\mathrm{v}) \\

\Rightarrow \frac{d v}{d x}=\mathrm{v}^{2}+1 \\

\Rightarrow \frac{d v}{v^{2}+1}=\mathrm{d} \mathrm{x}

Integrating on both the sides, we get,

\int \frac{d v}{v^{2}+1}=\int \mathrm{d} \mathrm{x}

\Rightarrow \tan ^{-1}v=x+c                                                                \left ( \because \frac{dx^{2}}{x^{2}+1}=\tan ^{-1}x \right )

Putting v=x+y, we get

            \Rightarrow \tan ^{-1}\left ( x+y \right )=x+c

            \Rightarrow x+y=\tan \left ( x+c \right )

                        (This is the required solution).

 

Posted by

infoexpert21

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