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  3. 9. for the differential equation: ??? + 2?? + 5? =

9. For the differential equation: ??? + 2?? + 5? = ?(?) (a) Write down the...

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Advance Math

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)

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