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 23 maths textbook solution.

Answers (1)

Answer : \text { (d) } y \ln y=x y_{1}

Hint: Eliminate arbitrary constant by differentiating the given equation with respect to x

Given:  \begin{aligned} &y=e^{C x}\\ \end{aligned}                       ......(i)

Explanation : \frac{d y}{d x}=C e^{C x}

\Rightarrow y_{1}=C e^{C x}                                 ...(ii)

Now from (i)

\Rightarrow y_{1}= e^{C x}

Take logarithm on both sides

\begin{aligned} &\Rightarrow \log y=C x \log e \\ &\Rightarrow \log y=C x \\ &\Rightarrow C=\frac{\log y}{x} \end{aligned}

Put in (ii)

\begin{aligned} &\Rightarrow y_{1}=\frac{\log y}{x} y\; \; \; \; \; \; \; \quad\left[y=e^{c x}\right] \\ &\Rightarrow y \ln y=x y_{1} \end{aligned}

Posted by


View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support