Author Topic: Quiz6 LEC5101  (Read 627 times)

Victorwoshinidie

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Quiz6 LEC5101
« on: November 15, 2019, 05:29:21 PM »
Q: x' = (1 2
             -5 -1)x
Express the general solution of the given system of equations in terms of real_value functions.



det of (1−𝜆      2
           -5        −1−𝜆)   = 𝜆^2 + 9
𝜆1 = 3i, 𝜆2 = -3i
Consider 𝜆1 = 3i, N(P-3iI) = N(1- 3i      2                       
                                               -5       -1-3i)  = span[(-2,1-3i)]

Consider e3it(-2, 1-3i) = cos(3t) + isin(3t) (-2,1-3i) = (-2cos(3t),cos(3t) + 3sin(3t)) + i (-2sin(3t), sin(3t) - 3cos(3t))


Thus, the general solution of this system is 


x(t) = c1(-2cos(3t),cos(3t) + 3sin(3t)) + i c2(-2sin(3t), sin(3t) - 3cos(3t))