Get Answers to all your Questions

header-bg qa

Explain solution for  RD Sharma Class 12 Chapter 21 Differential Equation Exercise Multiple choice Question Question 54 maths textbook solution.

Answers (1)

Answer : (c) y e^{x}+x^{2}=C

Hint : Convert the given equation in the form of  \frac{d y}{d x}+P(x) y=Q(x)

Given : e^{x} d y+\left(y e^{x}+2 x\right) d x=0

Explanation : e^{x} d y=-\left(y e^{x}+2 x\right) d x

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

So, the given equation is linear in y

I F=e^{\int d x}=e^{x}

Hence, the general solution

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

\begin{aligned} &\Rightarrow y e^{x}=-x^{2}+C \\ &\Rightarrow y e^{x}+x^{2}=C \end{aligned}

Posted by


View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support