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The particular solution of the differential equation x d y+2 y d x=0, when x=2, y=1 is
(A) x y=4
(B) x^{2} y=4
(C) x y^{2}=4
(D) x^{2} y^{2}=4
maths | Maths
The particular solution of the differential equation x d y+2 y d x=0, when x=2, y=1 is
(A) x y=4
(B) x^{2} y=4
(C) x y^{2}=4
(D) x^{2} y^{2}=4

Correct option is

(B) x^{2} y=4

\mathrm{xdy}+2 \mathrm{ydx}=0

\Rightarrow \frac{\mathrm{dy}}{\mathrm{y}}+\frac{2 \mathrm{dx}}{\mathrm{x}}=0

On Integrating both sides, we get

\int \frac{\mathrm{dy}}{\mathrm{y}}+2 \int \frac{\mathrm{dx}}{\mathrm{x}}=\mathrm{C}_{1}

\log y+2 \log x=\log C

\log y \mathrm{x}^{2}=\log \mathrm{C}

\therefore \mathrm{x}^{2} \mathrm{y}=\mathrm{C}

When \mathrm{x}=2, \mathrm{y}=1, then \mathrm{C}=4

\therefore Particular solution is \mathrm{x}^{2} \mathrm{y}=4

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