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Help with initial value problem(IVP)

  1. Aug 4, 2011 #1
    Hello experts!

    As we know that there are 3 different general solutions of an ordinary differential equation depends on that what type of roots we've gotten in the solution, listed below.
    1) y(t)=c1em1t+c2em2t
    2) y(t)=c1emt+c2temt
    3) y(t)=c1eucos(v)+c2sin(v)


    Now 1st solution is used when discriminant i.e. D>0, 2nd is used when D=0 and 3rd is used when D<0

    But here is a question,
    y''+6y'+9y=0
    By solving we get roots,
    m1=-3 and m2=-3
    While discriminant is -30
    & book has used 2nd solution to solve it, if D<0 it must use 3rd solution.

    How do we choose correct solution? Does solution is according to nature of roots(discriminant) or m1 & m2?

    Thanks for your contribution.
     
  2. jcsd
  3. Aug 4, 2011 #2
    Discriminant is not -30, it is 6^2-4.1.9=0
     
  4. Aug 4, 2011 #3
    Ok.
    Thanks to light me the right way.
     
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