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

Anthony Kramer

Anthony Kramer

Answered question

2022-05-27

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

Answer & Explanation

nifeonibonitozg

nifeonibonitozg

Beginner2022-05-28Added 12 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

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?