9. For the differential equation: ??? + 2?? + 5? = ?(?)
(a) Write down the auxiliary polynomial associated to thisdifferential equation and find the roots of the auxiliarypolynomial.
(b) Find a basis for the real solution set of the associatedhomogeneous differential equation ??? + 2?? + 5? = 0.
(c) For each ?(?) that follows, write down the trial particularsolution to ??? + 2?? + 5? = ?(?), with undetermined coefficients.Do NOT solve the constants that arise in your trial solution.
(i) ?(?) = 120???
(ii) ??(??) = 68 cos(2?)
(iii) ??(??) = 3?
(iv) ??(??) = 75??? sin(2?)
(d) Find a particular solution to ??? + 2?? + 5? = 100 cos(2?)(show your work)
