Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

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

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

Answers (1)

Answer : y=C e^{-x}+\frac{1}{2}(\sin x-\cos x)

Hint: To solve this equation we use \int u v\; d x formula.

Give: \frac{d y}{d x}+y=\sin x

Solution : \frac{d y}{d x}+P y=Q

\begin{aligned} &P=1, Q=\sin x \\ \end{aligned}

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

\begin{aligned} &=e^{\int 1 d x} \\ \end{aligned}

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

\begin{aligned} &y I f=\int Q I f d x+C \\ &y e^{x}=\int \sin x e^{x} d x+C \\ &=I=\sin \int e^{x}-\int \frac{d}{d x} \sin x \int e^{x} d x d x \end{aligned}

\begin{aligned} &=I=\sin e^{x}-\int \cos x e^{x} d x \\ &=I=\sin e^{x}-\int \cos x-e^{x} d x+\int \sin x e^{x} d x \\ &=I=e^{x}[\sin x-\cos x]-I \end{aligned}

\begin{aligned} &=2 I=e^{x}(\sin x-\cos x) \\ &=I=\frac{e^{x}}{2}(\sin x-\cos x) \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 invites LOC submission for Class 12 re-exams 2026 in West Asian countries
anam-khan

CBSE Datesheet 2027 LIVE: Class 10, 12 board exam timetable soon; sample question papers, marking scheme
anam-khan

CBSE Answer Sheets: CIC tells board to charge photocopying fee as per RTI rules, amend circular

Latest Question