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Theorems for Differentiability

The different...

Question

The differential equation satisfied by $y = \frac{A}{x} + B$ is ( $A, B$ are parameters)

A

x^{2} y_{1} = y

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B

{x y}_{1} + 2 y_{2} = 0

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C

{x y}_{2} + 2 y_{1} = 0

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D

{x y}_{1} - 2 y_{2} = 0

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Solution

The correct option is D ${x y}_{2} + 2 y_{1} = 0$
$y = \frac{A}{x} + B$
$y_{1} = - \frac{A}{x^{2}}$
$x^{2} y_{1} = - A$
Again differentiating w.r.t. $x$
$2 x y_{1} + x^{2} y_{2} = 0$
$x y_{2} + 2 y_{1} = 0$

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