如何评估SymPy在初始条件下给出的常数？ [英] How to evaluate the constants SymPy gives with initial condition?

问题描述

如何从SymPy给我的微分方程的解中求出常数C1和C2？有初始条件f（0）= 0和f（pi / 2）= 3。

How can I evaluate the constants C1 and C2 from a solution of a differential equation SymPy gives me? There are the initial condition f(0)=0 and f(pi/2)=3.

>>> from sympy import *
>>> f = Function('f')
>>> x = Symbol('x')
>>> dsolve(f(x).diff(x,2)+f(x),f(x))
f(x) == C1*sin(x) + C2*cos(x)

我尝试了一些 ics 的东西，但是没有用。示例：

I tried some ics stuff but it's not working. Example:

>>> dsolve(f(x).diff(x,2)+f(x),f(x), ics={f(0):0, f(pi/2):3})
f(x) == C1*sin(x) + C2*cos(x)

顺便说一句：C2 = 0且C1 = 3。

By the way: C2 = 0 and C1 = 3.

推荐答案

有一个拉请求实现了初始/边界条件，该请求已合并并应在SymPy 1.2中发布。同时，可以这样求解常量：

There's a pull request implementing initial/boundary conditions, which was merged and should be released in SymPy 1.2. Meanwhile, one can solve for constants like this:

sol = dsolve(f(x).diff(x,2)+f(x),f(x)).rhs
constants = solve([sol.subs(x,0), sol.subs(x, math.pi/2) - 3])
final_answer = sol.subs(constants)

代码返回 final_answer 为 3.0 * sin（x）。

solve 可能会返回解决方案列表，在这种情况下，必须替换 constants [0] 等。在任何情况下（出于一致性考虑）要强制其返回列表，请使用 dict = True ：

solve may return a list of solutions, in which case one would have to substitute constants[0], etc. To force it to return a list in any case (for consistency), use dict=True:

constants = solve([sol.subs(x,0), sol.subs(x, math.pi/2) - 3], dict=True)
final_answer = sol.subs(constants[0])

如果方程式包含参数，则 solve 可能会或可能不会解决您想要的变量（C1和C2）。可以确保如下：

If the equation contains parameters, solve may or may not solve for the variables you want (C1 and C2). This can be ensured as follows:

constants = solve([sol.subs(x,0), sol.subs(x, math.pi/2) - 3], symbols('C1 C2'))

， dict = True 将强制输出的列表格式。

where again, dict=True would force the list format of the output.

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