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Provide solution for RD Sharma maths Class 12 Chapter 21 Differential Equation Exercise Multiple Choice Question Question 8 textbook solution.

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

Hint: Use variable separable method means Take the y terms one side and x terms on the other side.

Given : \frac{d y}{d x}=\frac{2 y}{x}

Explanation : \frac{d y}{d x}=\frac{2 y}{x}

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

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

Where c is a constant

Equation passes through point (1,1)

\begin{aligned} &1=C(1)^{2} \\ &C=1 \\ &y=x^{2} \end{aligned}


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