1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: First Order Linear Differential Equation - I can't solve it

  1. Sep 23, 2009 #1
    1. The problem statement, all variables and given/known data
    Solve the differential equation dx/dt = 0.63 - (9x / 2060).

    2. Relevant equations

    3. 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...
  2. jcsd
  3. Sep 23, 2009 #2


    User Avatar
    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.
  4. Sep 23, 2009 #3
    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 =/
  5. Sep 23, 2009 #4


    User Avatar
    Science Advisor
    Homework Helper

    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook