Question

(1 point) Solve the system 4 -2 dx II dt 10 -4 -3 with x(0) = -2 Give your solution in real form. Xı = -3cos(21)+(27sin(2t))/5 x2 = -2cos(2t)-11 sin(2t) An ellipse with counterclockwise orientation 1. Describe the trajectory.

Answer 1

x (0)2 -3 Co lher Values are dia 20/ 22-26 txos Ques) da dt For Az Trece A2 4-400 Det A2 4(-4) 1-2) (10) I 4 so Charecterstic equation is given by 2² (Trece A) & + Det Az d2+4=0 datzi so For daai (A-21]) x2 4-20 - 2 (4-20) 41-272 -4-2i 101, +(-4-21) 12 80 (4-21) 213277 xial, X222-si So for dadi eigen Vector is lo 2.2) ) ) so you ex: (02245-22 (-2:] Cosax tisin 2x 2 Cell 22e + Sen 2x +i (2 fin2 - Ces 2x) Y2 = y 2 e 21 (Cos 2t -i'fin 24) (2) 2 ti

2 Cosax - fin 2x 2 Cos2x + fin 20 ti (Cos2x =2&in 22) so Real and im afinely parks are independent solution. Cos 27 Sinza 2 Cos 20+ fin 28 2 fin 22 - Cosza 42 at rro :-) C) 1 it ₂ (3) 2 (=-3, C2 = - 4 -2= 2ci-Ca 222 01 +222(-3)+2 2-4 Cos 20 2 Cos2x+ Sinza -u Sin 2x 2 fin 211 - Coszx N -3 Cos2a-4 fin 2x -2 Cos 2x - 11 fin2x