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Help solving a second order ODE with repeated roots, !

  1. Mar 2, 2012 #1
    Help solving a second order ODE with repeated roots, urgent!

    I have a differential equaition

    d2y/dx2 - 6dy/dx + 9y = 0

    I have found the general solution to be

    y = (Ax + B)e3x

    Now I need to find the solutions to A and B so that...

    when y = 4, x = 0
    when y = 49.e15, x = 5

    I literally have no idea where to start with this question and I have this and a few others of a similar format due in a couple of hours, so any help is greatly appreciated. I understand the other methods for ODE's but I do not have any notes for this method and have been unable to find any resources online.

    Any help is greatly appreciated!!!

    Thanks,

    Adam
     
  2. jcsd
  3. Mar 2, 2012 #2

    ehild

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    Re: Help solving a second order ODE with repeated roots, urgent!

    Plug in y=4, x=0. You get an equation for the unknowns A and B. Then plug in y=49 e15, x=5 (simplify, do not evaluate!) It is an other equation for A, B. Two equations for two unknowns. Solve.

    ehild
     
  4. Mar 2, 2012 #3
    Re: Help solving a second order ODE with repeated roots, urgent!

    Thanks... I didn't think it would be that simple! I was going far too deep into this question.

    It's been a long night! haha
     
  5. Mar 2, 2012 #4

    ehild

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    Re: Help solving a second order ODE with repeated roots, urgent!

    Maths is simpler than you imagine:smile:

    ehild
     
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