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 #