I have a system of differential equations of the kind shown below, and I would like to know how to do a time integration for known initial conditions of variables $x$ and $y$:
$$\ddot{x}+\dot{x}\dot{y} +y = f(t)$$ $$\ddot{x}+\dot{x} +x +y = 0$$
where $f$ is a known function of time. I have ignored the parameters for each addend.
I have experience integrating "simple" ODEs, but here I do not know how to separate the variables and/or deal with $\dot{x}\dot{y}$.
Thank you!