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Need solution for  RD Sharma maths Class 12 Chapter 21 Differential Equation Exercise Multiple Choice Question Question 20 textbook solution.

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Answer: (d) Parabolas

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

Given:  2 x \frac{d y}{d x}-y=3

Explanation : 2 x \frac{d y}{d x}=3+y

\begin{aligned} &\Rightarrow 2\left(\frac{d y}{3+y}\right)=\frac{d x}{x} \\ &\Rightarrow 2 \log (3+y)=\log x+\log C \end{aligned}

\begin{aligned} &\Rightarrow \log (3+y)^{2}=\log C x \\ &\Rightarrow(3+y)^{2}=C x \end{aligned}

The solution represents the parabola.

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