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Using exponential function to solve a DE

  1. Feb 6, 2010 #1

    I have the equation [tex]y'' +4y = t~sin(t)[/tex]

    i know that you usually guess the solution by substituting y for a polynomial (or whatever the form of the right side is).

    But i want to do this by using the exponential function exp.

    so, set y to equal [tex]te^{it}[/tex]
    chain rule:[tex]y^{\prime} = 1 \cdot e^{it} +t \cdot ie^{it} = e^{it} +tie^{it}[/tex]

    [tex] y^{\prime\prime} = ie^{it} + ie^{it} \cdot ti + ie^{it} = 2ie^{it} \cdot ti + ie^{it}[/tex]

    hm, is this really correct?
    and how would you proceed?
  2. jcsd
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