(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find a particular solution.

1. y'' +4y = 4 cos (2t) (for this problem, the instructions tell me that the forcing term is a solution of the associated homogeneous solution)

2. y'' + 16 y = 3 sin (4t)

2. Relevant equations

3. The attempt at a solution

1. I guess that Acos (2t) + Bsin (2t) was a solution but it did not work out. I am thinking that since the roots to the characteristic polynomial are 2i with a multiplicity of two this means that a basis for the homogeneous solution space is { cos (2t) + sin (2t) , t cos (2t) + t sin (2t)}. So I am thinking a better guess should be A t^2 cos (2t) + B t^2 sin (2t). Is this correct?

2. For this one I guessed Acos (4t) + Bsin (4t) was a solution but it did not work out (provided that I did my computation correctly). Any suggestions?

Thanks!

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# ODE - having trouble using method of undetermined coefficients

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