
To begin this question I would first rewrite into a non-homogenous solution to find out what case I will be working with. Once I found my case I would then move on to step 2 and that is writing out my partial solution. Then I would begin to find Yp, in this solution just divide the roots on both sides to get the -24e^-2t over the roots, then plug in the variable D with the exponent -2 and solve to get the Yp value. Once that is completed all we have to do is put the solution together. The general solution is always y(t) = Yh(t) + Yp(t). That would then conclude my answer for all the parts within this question.
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