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ODE Solution Query

  1. Jan 12, 2009 #1
    1. The problem statement, all variables and given/known data

    This is a solution detailed in a past paper,


    2. Relevant equations
    Utilise an integrating factor to solve as detailed by myself here.

    3. The attempt at a solution

    It can be said that,


    Hence, the solution by employing an integrating factor would yield,



    The problem is that I'm having the extra 'beta' term as shown above. Any ideas?

  2. jcsd
  3. Jan 12, 2009 #2
    A more direct approach, solving the homogenous part:




    Now, my memory here is fuzzy but [tex]e^{-t/\beta+C} = e^{-t/\beta}+e^C[/tex] ??
  4. Jan 12, 2009 #3
    Ah, another small blunder, of course!

    Now, [tex]\int{e^{t/\beta}\,dt}=\beta e^{t/\beta}+C[/tex]. thus, the 'beta's cancel,

    [tex]e^{t/\beta}\theta=\theta_m e^{t/\beta}+C[/tex]

    Dividing by [tex]e^{t/\beta}[/tex], yields,

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