This presentation outlines solving second order differential equations (ode) with python. The solution is obtained numerically using the python scipy ode engine (integrate module), the solution is therefore not in analytic form but the output is as if the analytic function was computed for each time step. The method is generally applicable to solving a higher order differential equation with python as well.
We will use a series RLC circuit as our ordinary differential equations example.
# -*- coding: utf-8 -*- from scipy import integrate from pylab import * # for plotting commands def rlc(A,t): Vc,x=A V = 1.0 #voltageSource R = 5.0 L=100.0e-9 #100nH C = 1.0e-9 #1nF res=array([x,(V-Vc-(x*R*C))/(L*C)]) return res time = linspace(0.0,0.6e-6,1001) vc,x = integrate.odeint(rlc,[0.0,0.0],time).T i=1.0e-9*x figure() plot(time,vc) xlabel('t') ylabel('Vc') show()