How to you find the general solution of $(2+x)y'=3y$ ?

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Answer 1 · 2017-02-16T09:52:25

$y = A(x+2)^3$

We have;

$(2+x)dy/dx = 3y$

This is a First Order separable Differential equation, and we can rearrange as follows:

$1/ydy/dx = 3/(x+2)$

And we can "separate the variables" to get:

$int \ 1/y \ dy = int \ 3/(x+2) \ dx$

This is straightforward to integrate:

$\ ln y = 3ln(x+2) + lnA$
$\ \ \ \ \ \ \= ln(x+2)^3 + lnA$
$\ \ \ \ \ \ \= lnA(x+2)^3$
$:. y = A(x+2)^3$

How to you find the general solution of (2+x)y'=3y(2+x)y'=3y?