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(1 point) xi(t) Let x(t) = be a solution to the system of differential equations: x2(t)...

(1 point) xi(t) Let x(t) = be a solution to the system of differential equations: x2(t) xy(t) xz(t) –6 x (1) 2 xi(t) x2(t) 3

(1 point) xi(t) Let x(t) = be a solution to the system of differential equations: x2(t) xy(t) x'z(t) –6 x (1) 2 xi(t) x2(t) 3 x2(t) = If x(0) find x(t). 2 3 Put the eigenvalues in ascending order when you enter xi(t), x2(t) below. xi(t) = exp( t)+ expo t) x2(t) = exp( t)+ expl t)
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SOLUTIONS The given system can be written as Z!) -6 - 1 2 2C+) X2 Cf) 23 () -3 X(+) = AX(+) Eigen value equation for the coeHere R2 is free variable (by pivot) Hence con be chosen X2 = 1 T -2x-1=0 xp =-Y Hence ] Now eigen vector for d2=-5 [A+51]x soHence C [3] [***]8+42[] 31-12 =) 29 -C2 ct C2 >> - 1 G - 2=2 at = 3 - 9=10, C2 = -7 (CM)=10 [*]***--[;)]* x, (4) Hence X(t)=

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(1 point) xi(t) Let x(t) = be a solution to the system of differential equations: x2(t)...
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