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General solution to a simple ODE

  1. Jan 20, 2010 #1
    Whenever I am stuck I usually manage by sitting down and working on the problem and eventuall finding the solution, this one is bothering me too much and I don't have any class untill friday so no hope of finding out before then unless I ask here.

    Q: Find a general solution to the diff.eq:

    d[f(x)]/dx = bf(x). Given f(0) = 1 and f'(0) = 3 define constants and find a solution for f(x)


    Attempts:
    Stuck, used 2th order ODEs so much this thing confuses me.
     
  2. jcsd
  3. Jan 20, 2010 #2
    This is solved simply through seperation of variables:

    [tex]\frac{df}{dx}=bf[/tex]

    Therefore

    [tex]\frac{df}{f}=bdx[/tex]

    Performing indefinite integration over this gives you:

    [tex]ln(f)=bx+c[/tex]

    With c being arbitrary constant of integration
    And explicitly f is given by

    [tex]f(x)=ae^{bx}[/tex]

    Where I chose to rewrite the arbitrary constant e^c as a.

    Determining a and b from your additional conditions is a simple algebric exercise.
     
  4. Jan 20, 2010 #3
    Thank you!
     
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