NotImplementedError:初始条件产生的常量解太多[SymPy]

Question

我试图通过修改找到的this differential equation代码来解决here问题。

import sympy as sp

t = sp.symbols('t', real=True)
x = sp.Function('x', real=True)

diffeq = sp.Eq(x(t).diff(t), sp.sqrt(1 - x(t)**2)) 
res = sp.dsolve(diffeq, ics={x(0): 0})

math.se文章建议，分段函数满足方程，但也许我的代码没有添加所有必要的假设。我得到以下回溯：

Traceback (most recent call last):
  File "/usr/lib/python3.10/idlelib/run.py", line 578, in runcode
    exec(code, self.locals)
  File "/home/galen/testing.py", line 7, in <module>
    res = sp.dsolve(diffeq, ics={x(0): 0})
  File "/usr/lib/python3/dist-packages/sympy/solvers/ode/ode.py", line 639, in dsolve
    return _helper_simplify(eq, hint, hints, simplify, ics=ics)
  File "/usr/lib/python3/dist-packages/sympy/solvers/ode/ode.py", line 694, in _helper_simplify
    solved_constants = solve_ics([rv], [r['func']], cons(rv), ics)
  File "/usr/lib/python3/dist-packages/sympy/solvers/ode/ode.py", line 808, in solve_ics
    raise NotImplementedError("Initial conditions produced too many solutions for constants")
NotImplementedError: Initial conditions produced too many solutions for constants

如何更改代码以正确解决该代码？

Answer 1

首先，求解者将方程视为代数方程，即求解x'²=1-x²，而不是得到可能的分段解，而是完全解析解。

由于某些原因，没有实现返回可能的解决方案的元组，可以手动执行，请参阅https://stackoverflow.com/a/46979535/3088138。

res = sp.dsolve(diffeq)
sol = res.rhs
print([ sol.subs(coeffs) for coeffs in sp.solve(sol.subs(t,0), dict=True) ])

返回[sin(t), -sin(t)]。第二种是与给定形式的ODE不兼容的。