Given, ydx+(x y^2)dy=0 ydx=(y^2 x)dy dydx=yy^2 x integrating on both sides y+c=12ln |y^2 x|+c 2y=ln |y^2 x| ...

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Linear Differential Equations of First Order

Solve: ydx+...

Question

Solve: $y d x + (x - y^{2}) d y = 0$

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Solution

Given,

$y d x + (x - y^{2}) d y = 0$

$y d x = (y^{2} - x) d y$

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

integrating on both sides

$y + c = \frac{1}{2} ln | y^{2} - x | + c$

$2 y = ln | y^{2} - x |$

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