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Homework Help: Diff EQ question

  1. Feb 15, 2005 #1
    When you are trying to determine the general solution of a homogeneous linear ordinary differential equation, after you find the roots, how do you decide which goes with c1 and which goes with c2?

    example:

    y''-3y'+2y=0

    Factoring the auxiliary equation

    m^2-3m+2=0=(m-1)(m-2)

    is there some kind of convention as to which gets named as m1 and m2?
    It seems like every time I do one of these kinds of problems, my answer is the opposite of the books. Is there any difference between

    y=c1e^(x)+c2e^(2x) and y=c1e^(2x)+c2e^(x)?
     
  2. jcsd
  3. Feb 15, 2005 #2
    c1 and c2 are arbitrary constants which must be determined by initial conditions only. so there is no difference if you interchange them
     
  4. Feb 15, 2005 #3
    That's what I was hoping for, thanks.
     
  5. Feb 15, 2005 #4
    No, they have no different....... you can write it either way.....

    It depend on the publisher...
     
  6. Feb 15, 2005 #5

    dextercioby

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    Science Advisor
    Homework Helper

    Read the result from right to left.I'm sure it will coincide with yours...

    Daniel.
     
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