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Variable Separable Method

Solve y d...

Question

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

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Solution

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

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

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

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

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

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

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

Integration on both sides

$\int d (\frac{x}{y}) = \int 2 d y$

$\frac{x}{y} = 2 y + c$ .

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