Question: please help 5. (11 points) Give all linear1 second order, constant coefcient ODEs that have the function :s(t) = cos(2t) as a homogeneous solution and

please help

5. (11 points) Give all linear1 second order, constant coefcient ODEs that have the function :s(t) = cos(2t) as a homogeneous solution and the function 220:) = 3132 as a particular solution. In addition, give for each such ODE the initial conditions 1(0) = In and 32"(0) = 190 that ensure that 1(t) = cos(2t) + 31:2 is the unique solution to the corresponding IVP

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