Science:Math Exam Resources/Courses/MATH152/April 2022/Question B4 (b)/Hint 1

Recall that the general solution to a system of differential equations of this form is ${\textstyle {\vec {y}}(t)=c_{1}e^{\lambda _{1}t}{\vec {v}}_{1}+c_{2}e^{\lambda _{2}t}{\vec {v}}_{2}}$, where ${\vec {v}}_{1},{\vec {v}}_{2}$ are eigenvectors associated to the eigenvalues $\lambda _{1},\lambda _{2}$. The real and imaginary parts of these complex solutions are two real solutions.