Science:Math Exam Resources/Courses/MATH152/April 2017/Question B 04 (c)/Hint 1

The general solution to the system of linear first order differential equations of the form ${\frac {d{\mathbf {x}}}{dt}}=A{\mathbf {x}}$ can be written as:

${\mathbf {x}}=c_{1}{\mathbf {v}}_{1}e^{\lambda _{1}t}+c_{2}{\mathbf {v}}_{2}e^{\lambda _{2}t}$

for eigenvectors ${\mathbf {v}}_{i}$ and eigenvalues $\lambda _{i}$ of the matrix $A$, with arbitrary constants $c_{i}$.