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Laplace transform for an ODE

  1. Apr 3, 2010 #1
    1. The problem statement, all variables and given/known data

    Using laplace transform, solve:

    [tex]
    y'' - y = \frac{x^2-3x+2}{|x^2-3x+2|}[/tex]

    y(0)=y'(0)=0

    2. Relevant equations



    3. The attempt at a solution

    Just to know if I'm on the right path -
    Since the quadratic has 2 roots, at 1 and at 2, the entire thing can be equal to either 1 or -1, depends on x.
    So can I write it as:
    [tex]y'' - y = 1 -2u_{1}(x) + 2u_{2}(x)[/tex]
    ?


    Will this be correct?
     
  2. jcsd
  3. Apr 3, 2010 #2

    gabbagabbahey

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    Homework Helper
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    Are [itex]u_1(x)[/itex] and [itex]u_2(x)[/itex] supposed to represent the Heaviside step functions

    [tex]u_1(x)=\left\{\begin{array}{lr}0, & x<1 \\ 1, & x\geq 1\end{array}\right. \;\;\;\;\;\;\;\;\; u_2(x)=\left\{\begin{array}{lr}0, & x<2 \\ 1, & x\geq 2\end{array}\right.[/tex]

    ???

    If so, you need to be careful to exclude the two roots from the Domain of your final solution since [itex]y''-y[/itex] is indeterminant there. Other than that, it looks good to me.
     
  4. Apr 3, 2010 #3
    Yes, this is exactly what I meant.
    Thank you - just making sure I wasn't doing something stupid.
     
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