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Homogeneous Function

The solution ...

Question

The solution of differential equation $y d x + (x - y^{2}) d y = 0$

e^{\frac{y}{x}} = sin x + c

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y = c x log x

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x = \frac{y^{2}}{3} + \frac{c}{y}

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cos (\frac{y - 2}{x}) = a

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Solution

The correct option is C $x = \frac{y^{2}}{3} + \frac{c}{y}$
$y d x + (x - y^{2}) d y = 0$
$y d x + x d y - y^{2} d y = 0$
$d (x y) - y^{2} d y = 0$
Integrating, we have
$x y - \frac{y^{3}}{3} = c$

This can also be written as
$x = \frac{y^{3}}{3} + \frac{c}{y}$

Suggest Corrections

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