Question: glider model, classify solutions for all position k values

We have two differential equations that model a flight of a glider
               diff(theta(t),t) = (v(t)^2 - cos(theta(t)))/v(t),
               diff(v(t),t)      = -sin(theta(t)) - 0.4*v(t)^2 + k,

-- We're now going to look at a model with a propeller or a small engine attached.
-- v>0 is the speed of the glider through the air and we have also fixed the drag coefficient to be 0.4
-- the additional term k was added to account for the acceleration caused by our small engine.

>with(DEtools):
>with(plots):
>with(LinearAlgebra):

>phug:=[ diff(theta(t),t) = (v(t)^2 - cos(theta(t)))/v(t),
               diff(v(t),t)      = -sin(theta(t)) - 0.4*v(t)^2 + k,
               diff(x(t),t)      = v(t)*cos(theta(t)),
               diff(y(t),t)      = v(t)*sin(theta(t)) ];

>for k:=0.9 I found a maple sheet that discusses it for this one solution:
k=0.9.mw

Any ideas on where to even start?