Which equations are best suited for evaluation of numerical algorithms for solving of ordinary differential equations

In my advanced seminar, I have to implement and evaluate numerical methods for solving of ordinary differential equations. I need to run the implemented methods on the Raspberry Pi Board and evaluate the execution time as well as the accuracy of these methods. Are there any good examples of ordinary differential equations that I could use for evaluating of explicit and implicit methods? I've described and implemented the following numerical methods:

• explicit: Euler's method, Heun's method, Fourth Order Runge-Kutta
• implicit: Euler's method, Non Self Starting Heun's method, Milne's method
• You could construct examples from a known function as solution as described in Empirical error proof Runge-Kutta algorithm which you can expand into a detailed analysis of a method like in Numerov method in a numerical example. The general economics of the methods of different order I explored in Quick question about Runge-Kutta. – LutzL Feb 5 at 18:16
• @LutzL Thank! The provided posts are a very good point to start to solve my problem. I am considering only first order differential equations so I think, the examples from these posts can also be applied to test my numerical methods. – Samashki95 Feb 6 at 8:06