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

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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