In order to study various ODE solvers (Forward Euler, Runge-Kutta, linear multi-step methods etc.) I would need a collection of different ODEs that are Lipschitz. Is there such a thing as an online database or similar where I can find a collection of various differential equations?
The reason is that, as of yet I have 4 differential equations where I can change the parameters in order to generate different trajectories. For example, for this ODE: $$ \frac{\mathrm{d}y}{\mathrm{d}t} = yt^\alpha - \beta y, $$ I can generate different trajectories by changing the parameters $\alpha$ and $\beta$. However, doing this randomly and generating 200 trajectories, I might not always meet the Lipschitz condition. Therefore, it would be helpful to have many different dynamics, but I don't know how/where to find hundreds of ODEs? Any suggestions on how to get a collection of as many different ODEs as possible?