Get Answers to all your Questions

header-bg qa

Need solution for  RD Sharma maths Class 12 Chapter 21 Differential Equation Exercise Multiple Choice Question Question 18 textbook solution.

Answers (1)

Answer :  \text { (a) } x(y+\cos x)=\sin x+C

Hint: The equation is linear in y i.e. \frac{d y}{d x}+P(x) y=Q(x) \text { i.e.IF }=e^{\int P(x) d x}

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

Explanation : \frac{d y}{d x}+P(x) y=Q(x) \text { i.e.IF }=e^{\int P(x) d x}

\begin{aligned} &I F=e^{\int \frac{1}{x} d x} \\ &=e^{\log x} \\ &=x \end{aligned}

So, the solution of differential equation is

\begin{aligned} &y x=\int x \sin x d x+C \\ &\Rightarrow y x=-x \cos x+\int \cos x d x+C \end{aligned}                        [integrating by parts]

\begin{aligned} &\Rightarrow y x=-x \cos x+\sin x+C \\ &\Rightarrow y x+x \cos x=\sin x+C \\ &\Rightarrow x(y+\cos x)=\sin x+C \end{aligned}

Posted by


View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support