Sympy:求解具有初始条件误差的微分方程 [英] Sympy: solving differential equation with initial conditions error
问题描述
自 Sympy
1.2版以来,python Sympy
在给定一些初始条件的情况下,已实现了在简单的微分方程中求解常数的功能.我正在尝试测试此功能,但是不断收到我不知道如何解决的错误.
SinceSympy
version 1.2, python Sympy
has implemented the ability to solve for the constants in a simple differential equation, given some initial conditions. I was trying to test out this feature, but keep getting an error that I don't know how to solve.
文档表示初始条件的以下格式,我尝试遵循在实现该功能的实际拉取请求中指定的格式.这是代码和错误.
The documentation indicates the following format for initial conditions, and I tried to follow what was specified in the actual pull request that implemented the feature. Here is the code and the error.
import sympy as sp
t = sp.symbols('t')
x = sp.Function('x')(t)
diffeq = sp.Eq(x.diff(t,t) - x, sp.cos(t))
res = sp.dsolve(diffeq, t, ics={x(0): 0,
x.diff(t).subs(t, 0): 0})
错误是:
Traceback (most recent call last):
File "<ipython-input-20-75c3e1d53138>", line 1, in <module>
res = sp.dsolve(diffeq, t, ics={x(0): 0, sp.diff(x(t), t).subs(t,0): 0})
TypeError: 'x' object is not callable
推荐答案
我不是sympy的重度用户,但我确实可以使用它-问题是,当您定义 x = sp.Function('x')(t)
时,您已经参数 t
传递给它,并且不能再在该行上为其传递 0
res = sp.dsolve(diffeq,t,ics = {x(0):0,sp.diff(x(t),t).subs(t,0):0})
-用(t)调用 x
使其成为定义函数".
I am not a heavy user of sympy, but I got that to work -
the problem is that when you define x = sp.Function('x')(t)
you already got
the parameter t
to it, and can no longer pass 0
for it at the line
res = sp.dsolve(diffeq, t, ics={x(0): 0, sp.diff(x(t), t).subs(t,0): 0})
-
The call of x
with (t) makes it a "defined function".
因此,将 x
保留为未定义函数,并在创建微分方程时仅在需要的点传递 t
即可:
So, leaving x
as an undefined function, and just passing t
for it in the points it is needed when creating the differential equation is the way to go:
import sympy as sp
t = sp.symbols('t')
x = sp.Function('x')
diffeq = sp.Eq(x(t).diff(t, t) - x(t), sp.cos(t))
res = sp.dsolve(diffeq, ics={x(0): 0, sp.diff(x(t), t).subs(t,0): 0})
(此外,尝试在第二个参数中传递 t
做dsolve会出现另一个错误.
(Also, trying to pass t
in the second parameter do dsolve gives another error. The docs tell that sympy should be able to correctly guess it, so I left it out - only to find the correct argument there would be x(t)
later)
这给了我res =
Eq(x(t), exp(t)/4 - cos(t)/2 + exp(-t)/4)
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