# Determine which of the following differential equations are separable. Do not solve the equations. y'=ln(xy)

opinaj 2022-09-01 Answered
Determine which of the following differential equations are separable. Do not solve the equations. ${y}^{\prime }=\mathrm{ln}\left(xy\right)$
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## Answers (1)

aveanoon
Answered 2022-09-02 Author has 8 answers
If differential equation can be written in the form
$\frac{dy}{dx}=g\left(x\right)f\left(x\right)$...(1)
then we can use separation of variables
${y}^{\prime }=\mathrm{ln}\left(xy\right)$
$\frac{dy}{dx}=\mathrm{ln}\left(xy\right)$
$⇒$ differential equation is not separable.
Result:
Differential equation is not separable.
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