This is good. I am finally convinced to install Gekko. At this time we are trying to do system identification of a non-linear second order system with 6 parameters and 5000 data samples. It works but it takes forever using orient. Odeint has a flaw. Our data is sampled every millisecond but the orient will use integration steps at odd increment to step from 0.000 to 0.001. There are two many steps. RK4 uses 4 steps. The bad part is that the odeint will cause a fault because it will do a step beyond 0.001 seconds. This is not a problem until we get to the end where is steps past the end of the time array and faults. We put a check in the "model" function to avoid faulting but this slows down the calculations even more and it is not clean. We gave up on odeint and switched to lmfit . Lmfit is faster but still slow. Our product uses lmfit and is very fast because it is written in C. Solutions are found in less than a second. Python is agonizingly slow by comparison. Python takes minutes. To speed up calculation we try using every 5th data point or more. If the step is too big we start getting NAN and INF results. tm=np.linspace(0,1,100) results in odd increments. tm=np.linspace(0,1,100+1) results in 10 ms increments. You need to try putting a print() in your model sometimes to see what it is doing. The video is good for teaching people how to get answers. I am writing this to let everyone know that in real life some of the things you learn are useless except for simple school problems and you really do need to understand what is happening inside the integration functions and not rely on something that someone else has written. I will let you know how Gekko works in real life.

Thank you for your effort ! I just wanted to ask what should I do to solve a second order non linear differential equations where there are variables in them calculated from an empirical formula ? I keep getting an attribute error : float ... I followed your reply here stackoverflow.com/questions/57038180/how-do-you-define-a-second-derivative-in-the-python-gekko-module but I have the problem that some variables in equations are calculated from empirical equations that are not function in time ... Thank you in advance

Differential equations are not always easy to solve, especially in Python. But if you're worried about having to solve ODEs, I have good news! I just saved myself from writing hundreds of lines of code by installing Gekko! "Gekko: 5 minutes of installation could save you 500 lines of code, or more."