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

##### 1 Answer

Feb 16, 2017

#### Explanation:

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 #