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Undetermined Coefficients / Variation of Parameters

  1. Nov 9, 2005 #1
    I know how to solve the following ODE with variation of parameters:

    [tex]y''+4y=4\sec{\left(2t\right)}.[/tex]

    Is there any way to solve this with undetermined coefficients? So far I have tried Yp=Acos(2t)+Bsin(2t), but that didn't work.

    Thanks for the help.
     
  2. jcsd
  3. Nov 9, 2005 #2
    Now that I try different methods, it seems that reduction of order won't work. At least, I come up with a function I can't integrate:

    Y=vyh

    v'=u

    [tex]u=\frac{2c_1t-2c_2\ln{\left(\cos{2t}\right)}}{c_1\cos{2t}+c_2\sin{2t}}[/tex]
     
  4. Nov 10, 2005 #3

    saltydog

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    The method of undetermined coefficients is applicable only if the RHS of the non-homogeneous equation is itself a particular solution of some homogeneous linear differential equation with constant coefficients. Since Sec(2t) is not such a solution, this method is not applicable.
     
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