使用Sympy绘制微分方程的解决方案

发布于 2025-02-12 21:21:33 字数 469 浏览 1 评论 0原文

from sympy import *
import sympy as sp
from sympy.abc import *
import numpy as np
import matplotlib.pyplot as plt

x=sp.Function('x')
t=symbols('t')
w=int(input("enter the frequency in hz"))
eq= sp. Eq(x(t).diff(t,2)+w**2*x(t)-f*sp .cos(w*t),0)
c= sp. dsolve(eq,x(t),ics={x(0):0,x(t).diff(t).subs(t,0):sp .cos(w*t)})
d= lambdify(t,c,'numpy')
n= np. arange (0,10,1)
y=d(n)

输出错误：

名称'x'未定义！

如何纠正此错误？

原文

from sympy import *
import sympy as sp
from sympy.abc import *
import numpy as np
import matplotlib.pyplot as plt

x=sp.Function('x')
t=symbols('t')
w=int(input("enter the frequency in hz"))
eq= sp. Eq(x(t).diff(t,2)+w**2*x(t)-f*sp .cos(w*t),0)
c= sp. dsolve(eq,x(t),ics={x(0):0,x(t).diff(t).subs(t,0):sp .cos(w*t)})
d= lambdify(t,c,'numpy')
n= np. arange (0,10,1)
y=d(n)

Output Error :

name 'x' is not defined!

How to rectify this error?

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我一向站在原地 2025-02-19 21:21:33

首先，如果打印出c，则获得eq（x（t），（f*t/880 + cos（440*t）/440）*sin（440* t））。要绘制，您需要通过c.rhs获得此方程的右手侧。

另请注意，（再次，打印）您在c.rhs中仍然具有符号f，我们应该用您的数值替换（我将手动输入替换为<<代码> W = 440 ）。这样就可以使我们c.rhs.subs（f，w）。

然后，lambdify正确执行，为我们提供了一个纯粹的数值值，而不是符号值，我们可以通过plt.plot（n，y）来绘制这些值。

总而言之，

[nav] In [29]: from sympy import *
          ...: import sympy as sp
          ...: 
          ...: from sympy.abc import *
          ...: import numpy as np
          ...: 
          ...: import matplotlib.pyplot as plt
          ...: x=sp.Function('x')
          ...: 
          ...: t=symbols('t')
          ...: w=440
          ...: 
          ...: eq= sp. Eq(x(t).diff(t,2)+w**2*x(t)-f*sp .cos(w*t),0)
          ...: c= sp. dsolve(eq,x(t),ics={x(0):0,x(t).diff(t).subs(t,0):sp .cos(w*t)})
          ...: 
          ...: d= lambdify(t,c.rhs.subs(f, w),modules='numpy')
          ...: n= np. arange (0,10,1)
          ...: 
          ...: 
          ...: y=d(n)
          ...: plt.plot(n, y)
          ...: plt.show()

First up, if you print out your c, you get Eq(x(t), (f*t/880 + cos(440*t)/440)*sin(440*t)). For plotting, you need to get the right hand side of this equation via c.rhs.

Also note that (again, printing) you still have the symbolic f in your c.rhs, which we should replace with your numerical value (I replaced the manual input with w = 440). So that gets us c.rhs.subs(f, w).

Then lambdify executes correctly, giving us an array of purely numerical values, rather than symbolic ones, which we can plot via plt.plot(n, y).

All in all,

[nav] In [29]: from sympy import *
          ...: import sympy as sp
          ...: 
          ...: from sympy.abc import *
          ...: import numpy as np
          ...: 
          ...: import matplotlib.pyplot as plt
          ...: x=sp.Function('x')
          ...: 
          ...: t=symbols('t')
          ...: w=440
          ...: 
          ...: eq= sp. Eq(x(t).diff(t,2)+w**2*x(t)-f*sp .cos(w*t),0)
          ...: c= sp. dsolve(eq,x(t),ics={x(0):0,x(t).diff(t).subs(t,0):sp .cos(w*t)})
          ...: 
          ...: d= lambdify(t,c.rhs.subs(f, w),modules='numpy')
          ...: n= np. arange (0,10,1)
          ...: 
          ...: 
          ...: y=d(n)
          ...: plt.plot(n, y)
          ...: plt.show()

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