Python - Differential equation, initial condition problem

Question

I am trying to implement a function that controls the differential equation.

Answer 1

To do this, you have to use a so called finite-state machine. This basically means you have to store a state which can change depending on the input, and affects the output.

In this case:

#State variable
qout_state = 0

def Qout(yrez):
    #Declare that we will be using the global variable
    global qout_state

    #If the input is >= 5, change the state to 1 and return 2.
    if yrez >= 5:
        qout_state = 1
        return 2

    #If the input is <= 1, change the state to 0 and return 0.
    if yrez <= 1:
        qout_state = 0
        return 0

    #If the input doesn't make any of the previous statements true, use the stored state:
    #If the state is 1, it means that the previous input wasn't <= 1, so we are on "return 2" mode
    if qout_state == 1:
        return 2
    #If the state is 0, it means that the previous input wasn't >= 5, so we are on "return 0" mode
    if qout_state == 0:
        return 0

Visual representation: