Say I have the 2-D system of ODEs as such:
$x' = y$
$y' = -2\left[Z(x) + y^2\right]y - Z'(x)$
and I wanted to write this as a single ODE, even though it won't help me at all in solving this system, I know! Is it valid to write:
$x = \int y dt$,
and then sub this into the $y'$ ODE and write:
$y' = -2\left[Z(\int y dt) + y^2\right]y - Z'(\int y dt)$
, so that you have one ODE in terms of one variable, $y$ in this case, where $Z$ is some function.