What is a solution to the differential equation $(2+x)y'=2y$ ?

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Answer 1 · 2016-07-07T21:37:49

$y = beta (2+x)^2$

this is separable

$(2+x)y'=2y$

$1/y y'=2/(2+x)$

$int \ 1/y \ dy=int \ 2/(2+x) \ dx$

$ln y = 2 ln (2+x) + alpha$

$ln y = 2 ln (2+x) + ln beta$

$ln y = ln beta(2+x)^2$

$y = beta (2+x)^2$

What is a solution to the differential equation (2+x)y'=2y(2+x)y'=2y?