# First Order Linear Differential Equation - I can't solve it

## Homework Statement

Solve the differential equation dx/dt = 0.63 - (9x / 2060).

## The Attempt at a Solution

I started by finding the integrating factor. So I integrated 9/2060, to get 9t/2060. Therefore e^(9t/2060) is my integrating factor.

Multiply 0.63 by that integrating factor to get 0.63e^(9t/2060) on the left side of the equation.

Integrate the left side, and you get 144.2e^(9x/2060). The right side of the equation looks like (e^(9t/2060))x right now.

I need this in a function of x so I divide by e^(9t/2060)... and I get x = 144.2.

But that doesn't make sense in the context of the question. What I have should be something that varies with t...

## Answers and Replies

Dick
Science Advisor
Homework Helper
You don't need an integrating factor. It's separable. You just have to integrate something of the form dx/(a+bx)=dt. It's just a log.

Oh... shouldn't it work the way I did it anyway though? I thought I could always use an integrating factor if I wanted to...

I can't figure out how to separate it =/

Dick
Science Advisor
Homework Helper
Oh... shouldn't it work the way I did it anyway though? I thought I could always use an integrating factor if I wanted to...

I can't figure out how to separate it =/

You can use an integrating factor if you do it half way carefully, sure. But where did t come from?? And how did it disappear at the end? You were being sloppy.

dx/(0.63 - (9x / 2060))=dt. There. It's separated. Now just integrate it.