# -*- coding: utf-8 -*-
# Método de Euler
import numpy as np
import matplotlib.pyplot as plt
#import math

def function(x,y):
    f=-x/y
    return f

def sol_exacta(x,y):
    g=sqrt(64-x**2)
    return g

x0=0
xf=8
y0=8
n=10
h=(xf-x0)/n


x=np.zeros(n)
y=np.zeros(n)
ye=np.zeros(n)

x[0]=x0
y[0]=y0
ye[0]=y0

print('x','y_euler','y_exacta')
print(x[0],y[0],ye[0])
for i in range(n-1):
    x[i+1]=x[i]+h
    y[i+1]=y[i]+h*function(x[i],y[i])
    ye[i+1]=sol_exacta(x[i+1],y[i+1])
    print(x[i+1],y[i+1],ye[i+1])
t=np.linspace(x0,xf,1000)
plt.plot(x,y,'b-')
plt.plot(t,sol_exacta(t,y),'g-')
plt.grid(true)
plt.show()