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Explain solution for  RD Sharma Class 12 Chapter 21 Differential Equation Exercise Multiple choice Question Question 52 maths textbook solution.

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Answer :  (c)y=cx

Hint: Use variable separable form  i.e. take y terms in one side and x terms to the other.

Given : \frac{y d x-x d y}{y}=0

Explanation : \frac{y d x}{y}-\frac{x d y}{y}=0

\begin{aligned} &\Rightarrow d x-\frac{x}{y} d y=0 \\ &\Rightarrow d x=\frac{x}{y} d y \\ &\Rightarrow \frac{d x}{x}=\frac{d y}{y} \end{aligned}

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

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