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 21 Difrential Equations excercise 21.6 question 1 maths textbook solution

Please solve RD  Sharma class 12 Chapter 21 Difrential Equations  excercise 21.6 question 1 maths textbook solution

Answers (1)

Answer: x+\frac{1}{2} \log \left|1+y^{2}\right|=C

Given:  \frac{d y}{d x}+\frac{1+y^{2}}{y}=0

Hint: Separate y and x and then integrate both sides.

Solution:

\begin{aligned} &\begin{aligned} \frac{d y}{d x}+\frac{1+y^{2}}{y} &=0 \\ \frac{d y}{d x} &=-\left(\frac{1+y^{2}}{y}\right) \end{aligned}\\ &\left(\frac{y}{1+y^{2}}\right) d y=-d x\\ &\text { [integrate both side] }\\ &\int\left(\frac{y}{1+y^{2}}\right) d y=-\int d x \end{aligned}

\begin{aligned} &\text { Let } 1+y^{2}=t\\ &\text { [differentiate with respect to } y \text { ] }\\ &\begin{aligned} 2 y d y &=d t \\ & \frac{1}{2} \int \frac{1}{t} d t=-\int d x \\ & \frac{1}{2} \log |t|=-x+C \\ & \frac{1}{2} \log \left|1+y^{2}\right|+x=C \end{aligned} \end{aligned}

 

Posted by

Infoexpert

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 2025 sees more in compartment, JNVs on top, perfect-scorers in minor subjects
anam-khan

Low score in CBSE results? Courses, career options after 12th open to you
anam-khan

CBSE class 10, 12 results: West Bengal CM Mamata Banerjee congratulates successful candidates

Latest Question