dripcima24

2022-09-07

What is a solution to the differential equation $\left(2+x\right)y\prime =2y$?

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Libby Weaver

Expert

this is separable
$\left(2+x\right)y\prime =2y$
$\frac{1}{y}y\prime =\frac{2}{2+x}$

$\mathrm{ln}y=2\mathrm{ln}\left(2+x\right)+\alpha$
$\mathrm{ln}y=2\mathrm{ln}\left(2+x\right)+\mathrm{ln}\beta$
$\mathrm{ln}y=\mathrm{ln}\beta {\left(2+x\right)}^{2}$
$y=\beta {\left(2+x\right)}^{2}$

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