Question

Note: You can earn partial credit on this problem Problem 3. (1 point) Solve the IVP der 43 dt 3 (0) = Give your solution in real form. Ij = I2 = Note: You can eam partial credit on this problem Problem 4.

Answer 1

Solve. We have matrix A= To find ilet eigen values of IA-AII = 0 1-4-3 (3 -4) -4-4 - 3 O 3 -471 =) 12+84 + 25 =0 - - O 64-9 XIX 25 - 4 31 2X1 To find 1,=-4+3i, let eigen value for TA - 2, I] V = 0 iv * Vi= Scanned with CamScanner

similarly for d2 = -4-31, we get The solution we get from first eigen value and eigen Kutor is xlt' = $947) + (4) 0411 = -4+ ē" ( cos(37) + i sin(34) ) lil - 414) = 4t I i cos(3x) - sin(3+) 1 I cos(3+) + isin (3+) ) - sin(34) -4 + los (31) Hle 241+1 e cs Scanned with CamScanner I cos13+) / sin 13t) /

21+1 = Ult) + ivet! Thus general solution is X(+) = GULH + C2 VIT) X(t) sin 4+ = C + Cey COS since X 10) = Sinie XIol= (%) , thus (3)=6:1*-() - (5) + C2 1 Thus X(+1= 5.401137, 1 € 4+ / -6 sin(36), Trė4+ 1.6 lost 3t) / \ 5 sin(34) W = 4+ ( 5 101(3+) - 6 sin(3+)) 1x scane with 6 los(34) + 5 sin (34) CamScanner
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