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Quadratic solution to ode

  1. Sep 21, 2008 #1
    1. The problem statement, all variables and given/known data
    Consider ax''+bx'+cx=0 for b^2-4ac=0 with k= -b/(2a).

    Show x=e^(kt) is a solution.

    3. The attempt at a solution

    x=e^(kt)
    x'=(-b/2a)e^((-b/2a)t)
    x''=(-b^2/4a^2)e^((-b/2a)t)

    Then i plugged these into ax''+bx'+cx=0 and simplified to get e^((-b/2a)t)(-((b^2)/2)+c)=0

    I'm stuck at what to do next.

    Thank you for any help.
     
  2. jcsd
  3. Sep 21, 2008 #2

    Defennder

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    Homework Helper

    To make things easier, don't use the k=-b/2a substitution until you're ready to compute the final answer. This helps to keep it a lot more tidier. Just subsitute the derivatives of x into the DE, factor out e^kt and make use of k = -b/2a as well as b^2 - 4ac = 0. It'll all cancel out to give 0.
     
  4. Sep 22, 2008 #3
    Ok, just got it. Thanks.
     
    Last edited: Sep 22, 2008
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