Is there a workaround for this? Using sympy 1.13.3 with python 3.13.1 when trying to solve y'(x)=y(x)^(1/3) with IC y(0)=1 it gives

NotImplementedError: Initial conditions produced too many solutions for constants

Does sympy really not able to solve this, or do I need some option or setting to use? I am new to using sympy for solving ode's. This ode is just quadrature ode, so I expected no problem solving it in sympy.

Here is complete code

python Python 3.13.1 (main, Dec 4 2024, 18:05:56) [GCC 14.2.1 20240910] on linux

from sympy import *
x=symbols('x')
y=Function('y')
dsolve(Eq(-y(x)**(1/3) + Derivative(y(x), x),0) , y(x), ics={y(0):1})

It gives

> Traceback (most recent call last):   File "<python-input-4>", line 1,
> in <module>
>     dsolve(Eq(-y(x)**(1/3) + Derivative(y(x), x),0) , y(x), ics={y(0):1})
>     ~~~~~~^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ 
> File "/usr/lib/python3.13/site-packages/sympy/solvers/ode/ode.py",
> line 640, in dsolve
>     return _helper_simplify(eq, hint, hints, simplify, ics=ics)   File "/usr/lib/python3.13/site-packages/sympy/solvers/ode/ode.py", line
> 709, in _helper_simplify
>     solved_constants = solve_ics([s], [r['func']], cons(s), ics)   File "/usr/lib/python3.13/site-packages/sympy/solvers/ode/ode.py",
> line 817, in solve_ics
>     raise NotImplementedError("Initial conditions produced too many solutions for constants") NotImplementedError: Initial conditions
> produced too many solutions for constants
> >>>

The solution should be

ode:=diff(y(x),x)=y(x)^(1/3);
dsolve([ode,y(0)=1])

#  y(x) = (9 + 6*x)^(3/2)/27

Is there a workaround for this? Using sympy 1.13.3 with python 3.13.1 when trying to solve y'(x)=y(x)^(1/3) with IC y(0)=1 it gives

NotImplementedError: Initial conditions produced too many solutions for constants

Does sympy really not able to solve this, or do I need some option or setting to use? I am new to using sympy for solving ode's. This ode is just quadrature ode, so I expected no problem solving it in sympy.

Here is complete code

python Python 3.13.1 (main, Dec 4 2024, 18:05:56) [GCC 14.2.1 20240910] on linux

from sympy import *
x=symbols('x')
y=Function('y')
dsolve(Eq(-y(x)**(1/3) + Derivative(y(x), x),0) , y(x), ics={y(0):1})

It gives

> Traceback (most recent call last):   File "<python-input-4>", line 1,
> in <module>
>     dsolve(Eq(-y(x)**(1/3) + Derivative(y(x), x),0) , y(x), ics={y(0):1})
>     ~~~~~~^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ 
> File "/usr/lib/python3.13/site-packages/sympy/solvers/ode/ode.py",
> line 640, in dsolve
>     return _helper_simplify(eq, hint, hints, simplify, ics=ics)   File "/usr/lib/python3.13/site-packages/sympy/solvers/ode/ode.py", line
> 709, in _helper_simplify
>     solved_constants = solve_ics([s], [r['func']], cons(s), ics)   File "/usr/lib/python3.13/site-packages/sympy/solvers/ode/ode.py",
> line 817, in solve_ics
>     raise NotImplementedError("Initial conditions produced too many solutions for constants") NotImplementedError: Initial conditions
> produced too many solutions for constants
> >>>

The solution should be

ode:=diff(y(x),x)=y(x)^(1/3);
dsolve([ode,y(0)=1])

#  y(x) = (9 + 6*x)^(3/2)/27

• python
• sympy

1 Answer 1

SymPy's dsolve can solve this when given without ics or other hints - is this what you were expecting?

>>> from sympy import *
>>> x = symbols("x")
>>> y = Function("y")
>>> exprs = dsolve(-y(x)**(1/3) + Derivative(y(x), x))
>>> exprs
[Eq(y(x), -2*sqrt(6)*(C1 + x)**(3/2)/9), Eq(y(x), 2*sqrt(6)*(C1 + x)**(3/2)/9)]
>>> for e in exprs:  # solve for C1 when y(0)=1
...   print(solve(e.rhs.subs({x:0}) - 1))
... 
[(sqrt(6)/4 - 3*sqrt(2)*I/4)**2, (sqrt(6)/4 + 3*sqrt(2)*I/4)**2]
[3/2]

Using SymPy 1.13.3 and passing x0=1 gives the same result

That said, I'm not absolutely certain why it doesn't like ics or how to better structure it