title: How to solve differential equation using Python builtin function odeint?
body: <p>I want to solve this differential equations with the given initial conditions:</p>
  
  <pre><code>(3x-1)y''-(3x+2)y'+(6x-8)y=0, y(0)=2, y'(0)=3
  </code></pre>
  
  <p>the ans should be <br><br>
  <code>y=2*exp(2*x)-x*exp(-x)</code></p>
  
  <p>here is my code:</p>
  
  <pre><code>def g(y,x):
      y0 = y[0]
      y1 = y[1]
      y2 = (6*x-8)*y0/(3*x-1)+(3*x+2)*y1/(3*x-1)
      return [y1,y2]
  
  init = [2.0, 3.0]
  x=np.linspace(-2,2,100)
  sol=spi.odeint(g,init,x)
  plt.plot(x,sol[:,0])
  plt.show()
  </code></pre>
  
  <p>but what I get is different from the answer.
  what have I done wrong?</p>