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Math Help - Differential equations

  1. #1
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    Exclamation Differential equations

    y” + ω^2y =f0 sinΏt

    The end part has really confused me and I would like some help please.
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by njr008 View Post
    y + ω^2y =f0 sinΏt

    The end part has really confused me and I would like some help please.
    first solve the homogeneous equation, y'' + \omega^2 y = 0 by assuming a solution y_h = e^{rt}

    then, let y_p = A \sin \Omega t + B \cos \Omega t

    find y_p'' and plug it into the original differential equation and solve for A and B by equating coefficients

    your final solution is y(t) = y_h + y_p
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