# -*- coding: utf-8 -*-
"""
@author: Ante
"""

import numpy as np
import matplotlib.pyplot as plt
from scipy.optimize import fsolve
from scipy.integrate import odeint

def f1(x):
    return np.sin(x)

def f2(x):
    return np.cos(x)

def f(x):
    return f1(x) - f2(x)

x = np.linspace(0, 20, 100)
plt.plot(x, f1(x), 'g', label='f1')
plt.plot(x, f2(x), 'r', label='f2')
plt.legend()

n = []
for i in range(3):
    n.append(fsolve(f, 3*i)[-1])
n = np.array(list(set(n)))
plt.scatter(n, f1(n), marker='o', color='blue')

plt.fill_between(x, f1(x), color='lightblue')

p1 = np.trapz(f1(x), x, dx=0.2)
p2 = np.trapz(f2(x), x, dx=0.2)
print('Razlika: ', p2-p1)

def dif_eq(z, t):
    return 3.2*z*np.sin(np.sqrt(z))

t = np.linspace(0, 10, 100)
z = odeint(dif_eq, [10, -1], t)
plt.figure()
plt.plot(t, z)