title: How to find the optimized parameters in an ODE in python?
body: <p>I am trying to obtain the optimized values of 5 parameters in a differential equation with Python.
  The equation is:</p>
  
  <pre><code>dl/dt = k1 * exp(((alpha * n * F) / (R * T)) * (V - (E * l) - phi)) - k3
  </code></pre>
  
  <p>The 5 parameters to obtain are: k1, alpha, E, phi, k3
  The constants are:</p>
  
  <pre><code>n = 3
  F = 96485
  R = 8.314
  T = 293
  V = 0.8
  </code></pre>
  
  <p>I have the values of lengths (l) in various times (t) as experiment results. That is:</p>
  
  <pre><code>t = [0, 120, 360, .......]
  l = [0, 0.09, 0.12, ......]
  </code></pre>
  
  <p>I also would like to assign bounds for each parameter.
  Is this procedure possible in Python?
  I wonder whether this should be done using scipy, platypus or any other library?
  Thank you in advance for your help.</p>