title: Solving system of coupled differential equations using scipy odeint
body: <p>I am a bit confused with <code>odeint</code>. </p>
  
  <p>I found one example below to solve <code>y"=ay + by'</code>. So it seems that <code>y[0]</code> is the function, <code>y[1]</code> is the first derivative. </p>
  
  <p>So does the following expression mean <code>y[1] =y'</code> and <code>y'[1]= a*y[0]+b*y[1]</code> ? </p>
  
  <p>If it were  <code>y[2], a*y[0]+b*y[1]</code>, what would it mean? </p>
  
  <p>I am a bit confused since the expression does not say the left hand side of the equation.</p>
  
  <p>I also encountered expressions like <code>[a(y[0], y[1]), b(y[0], y[1])]</code> but have no clue of the differential equation. </p>
  
  <p>Here is one example:</p>
  
  <pre><code>from scipy.integrate import odeint
  from pylab import * # for plotting commands
  
  def deriv(y,t): # return derivatives of the array y
      a = -2.0
      b = -0.1
      return array([ y[1], a*y[0]+b*y[1] ])
  
  time = linspace(0.0,10.0,1000)
  yinit = array([0.0005,0.2]) # initial values
  y = odeint(deriv,yinit,time)
  figure()
  plot(time,y[:,0])
  xlabel('t')
  ylabel('y')
  show()
  </code></pre>