import numpy as np
import matplotlib.pyplot as plt
import scipy.optimize as opt

#prvi zadatak
def difj(y,x):
    return -y+np.sin(100/(x**2+1))
x1 = np.linspace(0,20,100)
A,B = (0,5) , (0,-2)
y_a = np.ravel(odeint(difj, A[1],x))
y_b = np.ravel(odeint(difj,B[1],x))


#drugi zadatak
plt.plot(x1, y_a, label = 'y_a')
plt.plot(x1, y_b, label= 'y_b')
plt.legend()

#treci zadatak
p1 = np.trapz(y_a, x1, dx = 0.001)
p2 = np.trapz(y_b, x1, dx = 0.001)
print('Povrsina: ' abs(p2)-abs(p1) ) #kada se racuna povrsina mora biti abs
plt.fill_between(x1, y_a, y_b, color = 'lightgreen')

#cetvrti zadatak
x,y,z = np.loadtxt('rm-python_2.001.dat', delimiter = ' ', unpack = True)
plt.figure()
plt.plot(x,y,'r+')

#peti zadatak
r1 = np.poly1d(np.polyfit(x,y,2)) #2 oznacava 2.polinom
r2 = np.poly1d(np.polyfit(x,y,3)) #3 oznacava 3.polinom
plt.plot(x,r1(x),'g--')
plt.plot(x,r2(x),'b--')
plt.show()