Question

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I AM CURRENTLY IN DIFFERENTIAL EQUATIONS

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Consider a 3 x 3 linear system x' = Px where the coefficient matrix P has an eigenpair [-5 – 3i 1+ 3i, -1 Select a pair of real valued solutions from the following list: 3 + 3i i: et -5 sin 3t - 3 cos 3t - sin 3t 3 sin 3t + 3 cos 3t iii: et [3 sin 3t - 5 cos 3t - cos 3t 3 cos 3t – 3 sin 3t ii: et -5 sin 3t + 3 cos 3t] - sin 3t 3 sin 3t - 3 cos 3t [3 sin 3t - 5 cos 3t] iv: et - cos 3t 3 sin 3t – 3 cos 3t (a) (i) and (iv) (b) (iii) and (ii) (c) (ii) and (iv) (d) (i) and (iii)

Answer 1

For linear systeem x'= px eigenvalues of p is d=1+3i, eigemester ve F-5-31 given. 1 | 3+3i we know the Solution of such type of limeam System. is X = ent V. So putting the values of adv. x = (1+3) + (-5-3in e - esit cosat tisiu at -1 3+3i - et Bits-5-3i 3+3i --5-31 = et (cos Btt isiust) 3+31 et (Cassut + i sir st) (-5-31) ceszt - isinat (cosatt i sin st) (3 + 3i) - 5 casat + 3 sinat - 3 cosat - ssinat - surst tiet cosat 310s 3t - 3 siu at La cosat +3 siust (iii) (i) and (iiij. So option