Python中的三阶微分方程

Question

I am new to Python so that at this time, I can only very basic problems.

How do I solve an ODE like this in Python?

Answer 1

https://docs.scipy.org/doc/scipy-0.18.1/reference/generated/scipy.integrate.ode.html

Here the library you are searching for, if you scroll down on the bottom there are some examples too. Have a nice reading

Answer 2

Your solution could look like this (if you remove all plot related lines, it is quite short)

import numpy as np
from scipy.integrate import odeint
import matplotlib
matplotlib.use('Qt4Agg')
import matplotlib.pyplot as pl

# define the ODE as a first order system
def func(y,x):
    return [ 
        y[1], 
        y[2], 
        ( 7*x**1.5 - 5*x**2*y[2]-2*x*y[1] + 2*y[0]) / x**3 
        ]    

# initial values
y0=[ 10.6, -3.6, 31.2]
# points at which the solution value is requested
x = np.linspace(1,10,501)
# numerical integration
y=odeint(func, y0, x)
# y[-1,:] contains the value at x=10
print "[ y(10), y'(10), y''(10) ] = ", y[-1,:]

# plot the solution with subplots for each component
fig=pl.figure()
ax=fig.add_subplot(311)
ax.plot(x, y[:,0])
ax=fig.add_subplot(312)
ax.plot(x, y[:,1])
ax=fig.add_subplot(313)
ax.plot(x, y[:,2])
pl.show()