I am trying to model in python a second order ode problem, but I don't really get the notation.
Attached are the motion equations.
Are these 2 different ODEs? Is it ${\displaystyle \frac{d^2x}{dy^2}}$?
I know second order ODEs written in the form: ${\displaystyle \frac{d^2x}{dt^2} = \dots}$
But how should I interpret these two equation? Can it be written in another form? 
Those equations seem to be a model for the ballistic movement under aerodynamic forces. It can be resumed as
$$ v_x = \dot x\\ v_y = \dot y\\ \dot v_x = k \vert v\vert v_x\\ \dot v_y = -g + k\vert v\vert v_y\\ $$
with $\vert v\vert = \sqrt{v_x^2+v_y^2}$