from collections.abc import Iterator
from typing import Any, ClassVar

from sympy.core.cache import cached_property
from sympy.core.expr import Expr
from sympy.core.function import AppliedUndef, Function
from sympy.core.relational import Equality
from sympy.core.symbol import Symbol
from sympy.series.order import Order

class ODEMatchError(NotImplementedError): ...

class SingleODEProblem:
    eq: Expr = ...
    func: AppliedUndef = ...
    sym: Symbol = ...
    _order: int = ...
    _eq_expanded: Expr = ...
    _eq_preprocessed: Expr = ...
    _eq_high_order_free = ...
    def __init__(self, eq, func, sym, prep=..., **kwargs) -> None: ...
    @cached_property
    def order(self) -> int: ...
    @cached_property
    def eq_preprocessed(self) -> Expr: ...
    @cached_property
    def eq_high_order_free(self) -> Expr: ...
    @cached_property
    def eq_expanded(self) -> Expr: ...
    def get_numbered_constants(self, num=..., start=..., prefix=...) -> list[Symbol]: ...
    def iter_numbered_constants(self, start=..., prefix=...) -> Iterator[Symbol]: ...
    @cached_property
    def is_autonomous(self) -> bool: ...
    def get_linear_coefficients(self, eq, func, order) -> dict[int, Any | Order] | None: ...

class SingleODESolver:
    hint: ClassVar[str]
    has_integral: ClassVar[bool]
    ode_problem: SingleODEProblem = ...
    _matched: bool | None = ...
    order: list | None = ...
    def __init__(self, ode_problem) -> None: ...
    def matches(self) -> bool: ...
    def get_general_solution(self, *, simplify: bool = ...) -> list[Equality]: ...

class SinglePatternODESolver(SingleODESolver):
    def wilds(self): ...
    def wilds_match(self) -> list[Any]: ...

class NthAlgebraic(SingleODESolver):
    hint = ...
    has_integral = ...
    _diffx_stored: dict[Symbol, type[Function]] = ...

class FirstExact(SinglePatternODESolver):
    hint = ...
    has_integral = ...
    order = ...

class FirstLinear(SinglePatternODESolver):
    hint = ...
    has_integral = ...
    order = ...

class AlmostLinear(SinglePatternODESolver):
    hint = ...
    has_integral = ...
    order = ...

class Bernoulli(SinglePatternODESolver):
    hint = ...
    has_integral = ...
    order = ...

class Factorable(SingleODESolver):
    hint = ...
    has_integral = ...

class RiccatiSpecial(SinglePatternODESolver):
    hint = ...
    has_integral = ...
    order = ...

class RationalRiccati(SinglePatternODESolver):
    has_integral = ...
    hint = ...
    order = ...

class SecondNonlinearAutonomousConserved(SinglePatternODESolver):
    hint = ...
    has_integral = ...
    order = ...

class Liouville(SinglePatternODESolver):
    hint = ...
    has_integral = ...
    order = ...

class Separable(SinglePatternODESolver):
    hint = ...
    has_integral = ...
    order = ...

class SeparableReduced(Separable):
    hint = ...
    has_integral = ...
    order = ...

class HomogeneousCoeffSubsDepDivIndep(SinglePatternODESolver):
    hint = ...
    has_integral = ...
    order = ...

class HomogeneousCoeffSubsIndepDivDep(SinglePatternODESolver):
    hint = ...
    has_integral = ...
    order = ...

class HomogeneousCoeffBest(HomogeneousCoeffSubsIndepDivDep, HomogeneousCoeffSubsDepDivIndep):
    hint = ...
    has_integral = ...
    order = ...

class LinearCoefficients(HomogeneousCoeffBest):
    hint = ...
    has_integral = ...
    order = ...

class NthOrderReducible(SingleODESolver):
    hint = ...
    has_integral = ...

class SecondHypergeometric(SingleODESolver):
    hint = ...
    has_integral = ...

class NthLinearConstantCoeffHomogeneous(SingleODESolver):
    hint = ...
    has_integral = ...

class NthLinearConstantCoeffVariationOfParameters(SingleODESolver):
    hint = ...
    has_integral = ...

class NthLinearConstantCoeffUndeterminedCoefficients(SingleODESolver):
    hint = ...
    has_integral = ...

class NthLinearEulerEqHomogeneous(SingleODESolver):
    hint = ...
    has_integral = ...

class NthLinearEulerEqNonhomogeneousVariationOfParameters(SingleODESolver):
    hint = ...
    has_integral = ...

class NthLinearEulerEqNonhomogeneousUndeterminedCoefficients(SingleODESolver):
    hint = ...
    has_integral = ...

class SecondLinearBessel(SingleODESolver):
    hint = ...
    has_integral = ...

class SecondLinearAiry(SingleODESolver):
    hint = ...
    has_integral = ...

class LieGroup(SingleODESolver):
    hint = ...
    has_integral = ...

solver_map = ...