Solving a Differential equation in ODEINT

Question

I am going crazy and I cannot figure out what is wrong with my code. I am trying to solve a differential equation using ODEINT, but for some reasons it does not work as it supposed to, here is the question, it is a matrix of 5: equation

def model(y,t):
    
    #constant
    u = 7
    
    #l(t)
    l = 8.924 \
    - 1.584 * cos(math.radians((pi*t) / 1.51))\
    + 7.897 * sin(math.radians((pi*t) / 3.02))\
    - 10.434 * cos(math.radians((pi*t) / 4.53))\
    + 4.293 * cos(math.radians((pi*t) / 6.04))
    
    p0 = y[0]
    p1 = y[1]
    p2 = y[2]
    p3 = y[3]
    p4 = y[4]
    
    #Differential equations
    dp0dt = -l*p0 + u*p1
    dp1dt = l*p0 - (l+u)*p1 + u*p2
    dp2dt = l*p1 - (l+u)*p2 + u*p3
    dp3dt = l*p2 - (l+u)*p3 + u*p4
    dp4dt = l*p3 - u*p4
    
    return dp0dt, dp1dt, dp2dt, dp3dt, dp4dt

and here is the ODEINT and plot codes:

#initial condition
y0 = [1,0,0,0,0]

#time
time = np.linspace(0,8)

#solve ode
y = odeint(model,y0,time)

p0 = y[:,0]
p1 = y[:,1]
p2 = y[:,2]
p3 = y[:,3]
p4 = y[:,4]

#plot
plt.plot(time,p4)
plt.xlabel('time')
plt.ylabel('p4')
plt.show()

it should plot this: p4

Answer 1

The main problem is your use of math.radians in definiing function l . In math, almost invariably, arguments to cos etc are given in radians already. And if they involve pi then for sure they are in radians.

so I rewrote that bit as

    #l(t)
    l = 8.924 \
    - 1.584 * math.cos(math.pi*t / 1.51)\
    + 7.897 * math.sin(math.pi*t / 3.02)\
    - 10.434* math.cos(math.pi*t / 4.53)\
    + 4.293 * math.cos(math.pi*t / 6.04)

also your idents in the model function were wrong -- I took the liberty to fix them in the question as I assumed this was a copy and paste issue not your real code issue

with this fix I get this graph from your code

which to me looks kind of what you want