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Solution of ODE

  1. May 18, 2010 #1
    How can this equation be solved?

    [tex]\frac{dx}{dt}[/tex]=ax(b-x)
     
  2. jcsd
  3. May 18, 2010 #2

    Cyosis

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    Homework Helper

    By separation of variables.

    [tex]
    \frac{dx}{ax(b-x)}=dt
    [/tex]

    Now you can integrate both sides.
     
  4. May 19, 2010 #3
    The integral of the dx side requires decomposition into partial fractions.
     
  5. May 19, 2010 #4
    Many thanks!
    I'm a bit rusty in solving ODE's and was having a hard time trying to solve this one..
     
  6. May 22, 2010 #5
    dx/(ax(b-x)) = dx/abx + dx/ab(b-x)
    = dx/abx - d(b-x)/ab(b-x)
    and then you can integrate these terms.
     
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