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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