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  • Explain solution for RD Sharma Class 12 Chapter 21 Differential Equation Exercise Multiple Choice Question Question 23 maths textbook solution.

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}

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