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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

    Dick

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    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

    Dick

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    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.
     
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