I tried to solve system of two differential equations using scipy.integrate.odient.
The results are far from my expectations as one can see from the plots I attached below.
I would be grateful for any assistance.

I’m trying to solve a problem of filling and emptying of a retention behind a dam. What I’ve got are: 1) a function that relates the elevation of the water in the retention with the volume of the water, V(h); 2) a function that relates the discharge through the dam outlet with the water elevation, q(h); and 3) a function of water inflow given the duration of rain, Vr(tr).
For the case when I ignore the third function, i.e. I assume that V0 appears instantly in the reservoir, I managed to get the solution as:

I’d like to simulate a complex mecanical motion that goes from one phase to another in a strict interval of values for $deltaX$, where I’m finding a position X as a fucntion of time, which is calculated by different differential equations in two periodic domains, each for a relative change of X of length a and b. Is there a way to adapt ode or odeint from scipy, or should I program an alogrithm by hand?

I’m struggling to find a solution for these coupled differential equations:

I am trying to decelerate a rocket in space as it approaches Mars to enter its final orbit. I am trying to use solve_bvp to describe the position and the velocity of the rocket as it decelerates. The code is as follows.