The solution of the differential equatio

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Target Exam

CUET

Subject

-- Mathematics - Section A

Chapter

Differential Equations

Question:

The solution of the differential equation $2 x \frac{d y}{d x}-y=3$ represent

Options:

straight lines

circles

parabolas

ellipses

Correct Answer:

parabolas

Explanation:

$2 x \frac{d y}{d x}=y+3 \Rightarrow 2 \frac{d y}{y+3}=\frac{d x}{x}$

⇒ 2log(y + 3) = log x + log c

⇒ (y + 3)² = ex, which represent parabolas.

Hence (3) is the correct answer.