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Variable Separable Method

Find the solu...

Question

Find the solution of $x d y (y^{2} e^{x y} + e^{x / y}) = y d x (e^{x / y} - y^{2} e^{x y})$ .

- x y = log (e^{x / y} + c)

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x y = log (e^{- x / y} + c)

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- x y = log (e^{- x / y} + c)

No worries! We‘ve got your back. Try BYJU‘S free classes today!

x y = log (e^{x / y} + c)

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Solution

The correct option is D $x y = log (e^{x / y} + c)$
$x d y (y^{2} e^{x y} + e^{x / y}) = y d x (e^{x / y} - y^{2} e^{x y})$
Collect the terms of $e^{x y}$ and $e^{x / y}$
$y^{2} e^{x y} (x d y + y d x) = e^{x / y} (y d x - x d y)$
$e^{x y} (x d y + y d x) = e^{x / y} (\frac{y d x - x d y}{y^{2}})$
$e^{x y} d (x y) = e^{x / y} d (\frac{x}{y})$
Integrating both sides, we have $e^{x y} = e^{x / y} + c$ or $x y = log (e^{x / y} + c)$

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