TITLE: How to Solve the Coupled Differential Equations?
QUESTION [6 upvotes]: I came across the set of following coupled equations while studying cycloid motion in Griffiths' Intro to ED 
$\ddot{y}=\omega \dot{z}$
$\ddot{z}=\omega (\frac{E}{B}-\dot{y})$
I am at a loss as to how I may approach the problem to solve. Any help is appreciated.

REPLY [6 votes]: Let $q=\dot{y}$.  Then
$$\ddot{q} = \omega \ddot{z} = \omega^2 \left ( \frac{E}{B}-q\right)$$
or
$$\ddot{q}+\omega^2 q = \frac{E}{B} \omega^2$$
Can you solve this?