Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Explain solution for RD Sharma Class 12 Chapter 21 Differential Equation Exercise 21.10 Question 21 maths textbook solution.

Explain solution for RD Sharma Class 12 Chapter 21 Differential Equation Exercise 21.10 Question 21 maths textbook solution.

Answers (1)

Answer : y=x^{4}+x^{2} \log x+C x^{2}

Hint : To solve this we convert \text { If } \int Q I fformula.

Give : x d y=\left(2 y+2 x^{4}+x^{2}\right) d x

Solution : \frac{d y}{d x}=\frac{2 y+2 x^{4}+x^{2}}{x}

               \begin{aligned} &=\frac{d y}{d x}=\frac{2 y}{x}+2 x^{3}+x \\ \end{aligned}

               \begin{aligned} &=\frac{d y}{d x}-\frac{2 y}{x}=2 x^{3}+x \\ \end{aligned}

              \begin{aligned} &\frac{d y}{d x}+P y=Q \end{aligned}

               \begin{aligned} &P=-\frac{2}{x^{\prime}} Q=2 x^{3}+x \\ \end{aligned}

              \begin{aligned} &I f=e^{\int P d x} \\ \end{aligned}

              \begin{aligned} &=e^{-\int \frac{2}{x} d x} \\ \end{aligned}

              \begin{aligned} &=e^{=2 \log x} \\ \end{aligned}

               \begin{aligned} &=x^{-2} \end{aligned}

               \begin{aligned} &=\frac{1}{x^{2}} \; \; \; \; \; \; \; \; \quad\left[e^{\log x}=x\right] \\ \end{aligned}

               \begin{aligned} &=y I f=\int Q I f d x+C \\ &=\frac{y}{x^{2}}=\int \frac{2 x^{3}+x}{x^{2}} d x+C \\ &=\frac{y}{x^{2}}=\int 2 x+\frac{1}{x} d x+C \\ \end{aligned}

              \begin{aligned} &=\frac{y}{x^{2}}=x^{2}+\log x+C \\ \end{aligned}

               \begin{aligned} &=y=x^{4}+x^{2} \log x+C x^{2} \end{aligned}

 

 

Posted by

infoexpert23

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 supplementary practical exams from July 29; check exam guidelines, rules
anam-khan

CBSE Class 12 supplementary admit card out; exam on July 28 for over 2.5 lakh
anam-khan

CBSE Class 12 supplementary exams 2026 datesheet out; test on July 28

Latest Question