How to evaluate the constants SymPy gives with initial condition?

问题

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)

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)

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

回答1:

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)

The code returns final_answer as 3.0*sin(x).

Remarks

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])

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'))

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

来源：https://stackoverflow.com/questions/41192748/how-to-evaluate-the-constants-sympy-gives-with-initial-condition