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Reconstructing my notes

  1. May 28, 2005 #1
    I'm trying to rewrite my notes from my differential equations class last week. my proffesor asked us to write the charastic equation of this:[tex]y''-4y' +5y =0[/tex] is this correct?
    [tex]e^{2t}(C_1\cos{t} + C_2\sin{t})[/tex]
  2. jcsd
  3. May 28, 2005 #2


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    No, it's not- it's not even an equation! I would suggest you look up "characteristic equation" in your text book.
  4. May 28, 2005 #3

    i meant this.[tex]y=e^{2t}(C_1\cos{t} + C_2\sin{t})[/tex]
  5. May 28, 2005 #4


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    The characteristic equation is what you elsewhere call the auxiliary equation, if I'm not mistaken.
  6. May 28, 2005 #5


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    x^2 - 4x + 5, i.e. make every derivative a power, so you get x^2 -4x + 5x^0

    or just substitute y = e^(rt) then perform the derivatives in the given differential equation and you get the characteristic equation out front in terms of the variable r this time.
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