Which are good Ordinary differential equation (ODE) of second order to test a numerical integrator?

Question

Can someone give me new ODE's to test my code for viability?
https://code.sololearn.com/cLxPy2zgt1Zj/?ref=app

Answer 1

You can check the second order equation from the van der pol oscillator:
https://mathworld.wolfram.com/vanderPolEquation.html

There are many similar equations based on physics. You can also check for engine speed / temperature / pressure / (water) level control systems.