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))
