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 21.7 question 38 sub question (iv)

Provide solution for RD Sharma maths class 12 chapter Differential Equations exercise 21.7 question 38 sub question (iv)

Answers (1)

Answer: \frac{1}{2}\left(\tan ^{-1} x\right)^{2}+\log \left|1+y^{2}\right|=c

Hint: Separate the terms of x and y and then integrate them.

Given: \left(1+y^{2}\right) \tan ^{-1} x d x+2 y\left(1+x^{2}\right) d y=0

Solution:\left(1+y^{2}\right) \tan ^{-1} x d x+2 y\left(1+x^{2}\right) d y=0

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

        Integrating both sides

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

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 12 Board Exam 2026 LIVE: Accountancy paper starts; analysis, question papers with solutions soon
anam-khan

CBSE Class 12 Physics paper well-balanced, moderate in difficulty; MCQ lengthy, calculation-based
anam-khan

CBSE Board 2026 Exam LIVE: Class 12 physics 'moderate' in difficulty; set-wise answer key updates

Latest Question