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 Class 12 Chapter 21 Differential Equation Exercise 21.10 Question 20

Provide Solution for RD Sharma Class 12 Chapter 21 Differential Equation Exercise 21.10 Question 20

Answers (1)

best_answer

Answer:  2 y e^{\tan ^{-1} x}=e^{2 \tan ^{-1} y}+C

Hint: To solve this equation we use  I\int f\left ( x \right )dx  formula.

Give:  \left(1+x^{2}\right) \frac{d y}{d x}+y=e^{\tan ^{-1} x} \

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

\begin{aligned} & \\ &\quad=\frac{d y}{d x}+\frac{y}{\left(1+x^{2}\right)}=\frac{e^{\tan ^{-1} x}}{1+x^{2}} \ldots(i) \\\\ &\quad=\frac{d y}{d x}+P(x) y=Q x \end{aligned}

\begin{aligned} &P=\frac{1}{1+x^{2}}, Q=\frac{e^{\tan ^{-1} x}}{1+x^{2}} \\\\ &I f=e^{\int P d x} \\\\ &=e^{\int \frac{1}{1+x^{2}} d x} \\\\ &=e^{\tan ^{-1} x} \ldots(i i) \end{aligned}

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

=d\left(y e^{\tan ^{-1} x}\right)=\frac{e^{\tan ^{-1} x^{2}}}{1+x^{2}} d x \\\\
 

=y e^{\tan ^{-1} x}=\int \frac{e^{\tan ^{-1} x^{2}}}{1+x^{2}} d x+C

Posted by

infoexpert27

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 12th Result 2026 Date LIVE: Class 12 scores at cbse.gov.in soon; how to check, toppers list
anam-khan

CBSE 12th Result 2026 Date: Here’s what previous years’ trends indicate
anam-khan

CBSE Class 12th marks uploading for schools in West Asia starts from April 8

Latest Question