Given, xdydxy^2x+y=0 dydxy^2= y dydx= 1y integrating on both sides, we get, y= xy y^2+x=0 ...

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Solving Linear Differential Equations of First Order

x dy dx y 2 x...

Question

$x \frac{d y}{d x} \frac{y^{2}}{x} + y = 0$

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Solution

Given,

$x \frac{d y}{d x} \frac{y^{2}}{x} + y = 0$

$\frac{d y}{d x} y^{2} = - y$

$\frac{d y}{d x} = - \frac{1}{y}$

integrating on both sides, we get,

$y = - \frac{x}{y}$

$y^{2} + x = 0$

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