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Homework Help: 2nd order homogenous differential equation

  1. Mar 16, 2006 #1
    Solve the following for y(x);

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

    I kind of know what to do up to a point but after that I`m stuck (bad notes and no text book!!!).

    Here`s what i`ve done so far, if someone could hint as how to finish this question i should be able to do the other 9 I have.


    let y = e^rx then y' = r e^rx and y''= r^2 e^rx

    therefor

    r^2 e^rx -3re^rx + 2e^rx = 0

    or
    r^2 -3r +2 = 0

    or

    (r-2)(r-1)=0

    i.e. r=2 and r=1


    now i`m stuck!! What do i need to do to find the solution?

    (sorry about the lack of latex but my pc refuses to display it! so if you could not use it i would be gratefull)
     
  2. jcsd
  3. Mar 16, 2006 #2

    TD

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    Well, as you said you proposed solutions of the form [itex]y = e^{rx}[/itex] and you found r to be 2 and 1. A lineair combination of these solutions, together with two constants, is your complete solution to the homogenous equation.
     
  4. Mar 16, 2006 #3
    So i would have a solution something like

    y= A e^2x + B e^x

    How do I find A and B or is that an irrelavent question?
     
  5. Mar 16, 2006 #4

    TD

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    Your solution is fine and you cannot determine A and B, unless there are initial or boundary conditions. For a general n-th order DE, you'll have n constants.
     
  6. Mar 16, 2006 #5
    TD thank you very much, your help is gratefully received.
     
  7. Mar 16, 2006 #6

    TD

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    You're welcome :smile:
     
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