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Please solve RD Sharma Class 12 Chapter 21 Differential Equation Exercise Multiple Choice Question Question 29 maths textbook solution.

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Answer : \text { (a) } x=C y^{2}

Hint: Subtangent means \frac{\frac{y}{d y}}{d x} and abscissa means x

Given: Subtangent at any point of the curve doubles the abscissa.

Explanation: \frac{\frac{y}{d y}}{d x}=2 x    Correct the ratio 

\begin{aligned} &\Rightarrow y=2 x \frac{d y}{d x} \\ &\Rightarrow 2 \frac{d y}{y}=\frac{d x}{x} \end{aligned}

Integrate both sides

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

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