## MIT 1803 lecture 9

This lecture introduced linear second order ODEs, specifically

$y'' + Ay' + By = 0$

the approach is to try $y=e^{rt}$ and found the characteristic equation of the system.

N.B. complex roots of the quadratic equation are complex conjugates $a + bi$.

Theorem: if $u+iv$ is a complex solution to a real differential equation, then $u$ and $v$ are real solutions.