title: Issue with odeint from scipy.integrate when I start the range not at 0
body: <p>I am writing a program to solve a differential equation in the form x''(t) + w^2(t)*x(t) = 0 so i used odeint. However, whenever it doesn't start from 0, it puts the first point as to what 0 should have been</p>
  
  <p><a href="https://i.stack.imgur.com/86LsN.png" rel="nofollow noreferrer">sin(t) when starting from t = -1</a></p>
  
  <p><a href="https://i.stack.imgur.com/GMIsF.png" rel="nofollow noreferrer">sin(t) when starting from t = 0</a></p>
  
  <p>the pictures show the issues clearly</p>
  
  <pre><code>import numpy as np
  import matplotlib.pyplot as plt
  from scipy.integrate import odeint
  
  
  def omega(t):
      return 1
  
  
  def dU_dt(U, t):
      return [U[1], -U[0] * ((omega(t)) ** 2)]
  
  
  x0 = 0  # This is the initial condition x(0)
  x1 = 1  # This is the initial condition x'(0)
  
  U0 = [x0, x1]
  
  pi = np.pi
  
  start = -1
  stop = 2 * pi
  N = 10 ** 2
  
  xs = np.linspace(start, stop, N)
  Us, info = odeint(dU_dt, U0, xs, rtol=1e-10, full_output=True)
  ys = Us[:, 0]
  
  plt.xlabel('t')
  plt.ylabel('x')
  plt.axvline(x=0.0, color=(0, 0, 0))
  plt.axhline(y=0.0, color=(0, 0, 0))
  plt.plot(xs, ys)
  
  for i in range(len(xs)):
      print(xs[i], ys[i])
  
  plt.show()
  
  </code></pre>