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Thread: ODE resonance clarification

  1. #1
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    ODE resonance clarification

    I tried using an online calculator for y''-3y'+2y=2x+4e3x and the answer they gave was y=c1e2x+c2ex+x+1.5+2e3x .However, isn't the yp part wrong as the answer neglected the fact that there is resonance?
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  2. #2
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    Re: ODE resonance clarification

    There is no resonance. The roots of the characteristic polynomial are 1 and 2, not 3.
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  3. #3
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    Re: ODE resonance clarification

    I see, but could 2 in 2x not be considered as a root?
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  4. #4
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    Re: ODE resonance clarification

    No. The right hand side has nothing to do with the characteristic polynomial.

    The roots 1 and 2 give terms in $e^{x}$ and $e^{2x}$ to form the complementary solution. These could only resonate with forcing terms (the right hand side) in $e^{x}$ and $e^{2x}$ respectively.
    Last edited by Archie; Jun 21st 2019 at 12:49 PM.
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