Coupled Differential Equations

Problem:



Solution:

$ x = \left[\begin{array}{c} \frac{1}{2}e^{(1+4i)t} - \frac{1}{2} e^{(1-4i)t} + e^{6t} + \frac{4}{17} \\ \frac{1}{2}e^{(1+4i)t} + \frac{1}{2} e^{(1-4i)t} + t + e^{6t} + \frac{1}{17} \end{array}\right] $