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

excefebraxp 2022-09-12 Answered
How to you find the general solution of ( 2 + x ) y = 3 y ?
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Answers (1)

Peyton Cox
Answered 2022-09-13 Author has 18 answers
We have;

( 2 + x ) d y d x = 3 y

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

1 y d y d x = 3 x + 2

And we can "separate the variables" to get:

  1 y   d y =   3 x + 2   d x

This is straightforward to integrate:

  ln y = 3 ln ( x + 2 ) + ln A
            = ln ( x + 2 ) 3 + ln A
            = ln A ( x + 2 ) 3
y = A ( x + 2 ) 3
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