Question

solve the system then its asking to give the solution in real form and i am stuck.

ELLIPSE COUNTERCLOCKWISE ELLIPSE COUNTERCLOCKWISE (10 points) Solve the system 6 -3 with x(0) = Give your solution in real form. 2 = 3 22 = 3 An ellipse with counterclockwise orientation 1. Describe the trajectory. Note: You can earn partial credit on this problem.

Answer 1

Give system 1st thing we need to do is to brood eisen vales bor hemania 1AA/= | [ 21 - [ ] (-3) 215 - (6-7) (-6-7) - -- [36-x] +hS ax +9 =0 -9 ad- #31 Next we need eisen veckor vire. we solie (A-XI) v = 0 - let v = [a, bor da si ecuation become 16-3i - 3 15 - = (2-ija, -(6-3i)a, -3an = o A2 = 6-31 jan and 15 a, & (6+3i) a2=0 and a

By usiz 1st canation. Ist eigen rechr via bat asam urche une certa [3,4- agal (2-c)an Now by using and eanatin (6+3i) a = -isa,. ar=-(6+31) az=- (2+i az and eiges vecho m . - (be ak Vza will be can dasaleobis, Veri Ft 10 years 2 ti solution bron 1st eiger redor vi ni (3)= edt VI. = eBit ri7 2 - ľ Now it = (cas (3+) + i sin3+) ni (t)= (Cup3t+ i sin3r cu I 2 -i حوری ) + طلابها L 2005 3t & Sin3t - i (cas 3+ - zsinat |

Sint ni (t)= ((st 251n3t - Cosat Laast +Sin3t ů (2- & (t) tir (+) General solution to år (t)= e, . ů (8) + C₂ J (7) Sin3+ Cost 2 os3t+Sinat ) Izsinat - Cool Now we have to apples initial condition (0)=(3) (2) - e. She on Somo)- cz (esimo too) = { (²) = cc (2) + 2 ( 0) = (2-4) c.= 3, 20, - ca 2 - 60 car - 1 ere 7 solution - 3 (cast .nl +7 12 cos32+ sinat) singe 12 5103t – Cosat (osat ( Sin3t 2 Ginat -653 . ni 7 3 2 cast M & Sinat =