## Bibliothèques
import numpy as ...
import matplotlib.pyplot as ...
import random as rd

## 1
a, b = ..., ...
y_0, n = 1, 255
t, y  = [a], [y_0]
h = ...
for k in range(...):
    y.append(y[k] + ...)
    t.append(...)
plt.plot(..., ...)
plt.show()

## 2


## 3
def F(t,y):
    return ...

a, b, y_0 = ..., ..., ...
for ... in [10,100,1000]:
    t, y = ...
    legende = "n = " + str(...)
    plt.plot(..., ..., label = legende)
plt.plot(..., np.exp(t), label= "exp")
plt.legend(loc = "best")
plt.show()

## 4


## 5
def F(t,y):
    return ...

a, b, y_0 = ...
n = 10

... = euler(...)
plt.plot(...,label = "Euler, n=10")

... = heun(...)
plt.plot(...,label="Heun, n=10")

... = rk4(...)
plt.plot(t,y,label="RK4, n=10")

plt.plot(..., label="exp")

plt.legend(loc = "best")
plt.show()


## 8


## 9
a, b= ...
alpha, beta = ...
delta, gamma = ...
n = ...
fig, (ax1, ax2) = plt.subplots(2)
x0 = ...
y0 = ...
t, x, y =  lotkaVolterra(...)
ax1.plot(...)
ax2.plot(...)
ax1.set_ylabel("proies")
ax2.set_ylabel("prédateurs")
plt.show()

## 10