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ODE

.. automodule:: sympy.solvers.ode

User Functions

These are functions that are imported into the global namespace with from sympy import *. These functions (unlike Hint Functions, below) are intended for use by ordinary users of SymPy.

dsolve

.. autofunction:: sympy.solvers.ode::dsolve

dsolve_system

.. autofunction:: sympy.solvers.ode.systems::dsolve_system

classify_ode

.. autofunction:: sympy.solvers.ode::classify_ode

checkodesol

.. autofunction:: sympy.solvers.ode::checkodesol

homogeneous_order

.. autofunction:: sympy.solvers.ode::homogeneous_order

infinitesimals

.. autofunction:: sympy.solvers.ode::infinitesimals

checkinfsol

.. autofunction:: sympy.solvers.ode::checkinfsol

constantsimp

.. autofunction:: sympy.solvers.ode::constantsimp

Hint Functions

These functions are intended for internal use by :py:meth:`~sympy.solvers.ode.dsolve` and others. Unlike User Functions, above, these are not intended for every-day use by ordinary SymPy users. Instead, functions such as :py:meth:`~sympy.solvers.ode.dsolve` should be used. Nonetheless, these functions contain useful information in their docstrings on the various ODE solving methods. For this reason, they are documented here.

allhints

.. autodata:: sympy.solvers.ode::allhints

odesimp

.. autofunction:: sympy.solvers.ode.ode::odesimp

constant_renumber

.. autofunction:: sympy.solvers.ode.ode::constant_renumber

sol_simplicity

.. autofunction:: sympy.solvers.ode.ode::ode_sol_simplicity

factorable

.. autoclass:: sympy.solvers.ode.single::Factorable
   :members:

1st_exact

.. autoclass:: sympy.solvers.ode.single.FirstExact
   :members:

1st_homogeneous_coeff_best

.. autoclass:: sympy.solvers.ode.single::HomogeneousCoeffBest
   :members:

1st_homogeneous_coeff_subs_dep_div_indep

.. autoclass:: sympy.solvers.ode.single::HomogeneousCoeffSubsDepDivIndep
   :members:

1st_homogeneous_coeff_subs_indep_div_dep

.. autoclass:: sympy.solvers.ode.single::HomogeneousCoeffSubsIndepDivDep
   :members:

1st_linear

.. autoclass:: sympy.solvers.ode.single::FirstLinear
   :members:

2nd_linear_airy

.. autoclass:: sympy.solvers.ode.single::LinearAiry2nd
   :members:

2nd_linear_bessel

.. autoclass:: sympy.solvers.ode.single::LinearBessel2nd
   :members:

Bernoulli

.. autoclass:: sympy.solvers.ode.single::Bernoulli
   :members:

Liouville

.. autoclass:: sympy.solvers.ode.single::Liouville
   :members:

Riccati_special_minus2

.. autoclass:: sympy.solvers.ode.single::RiccatiSpecial
   :members:

nth_linear_constant_coeff_homogeneous

.. autoclass:: sympy.solvers.ode.single::NthLinearConstantCoeffHomogeneous
   :members:

nth_linear_constant_coeff_undetermined_coefficients

.. autoclass:: sympy.solvers.ode.single::NthLinearConstantCoeffUndeterminedCoefficients
   :members:

nth_linear_constant_coeff_variation_of_parameters

.. autoclass:: sympy.solvers.ode.single::NthLinearConstantCoeffVariationOfParameters
   :members:

nth_linear_euler_eq_homogeneous

.. autoclass:: sympy.solvers.ode.single::NthLinearEulerEqHomogeneous
   :members:

nth_linear_euler_eq_nonhomogeneous_variation_of_parameters

.. autoclass:: sympy.solvers.ode.single::NthLinearEulerEqNonhomogeneousVariationOfParameters
   :members:

nth_linear_euler_eq_nonhomogeneous_undetermined_coefficients

.. autoclass:: sympy.solvers.ode.single::NthLinearEulerEqNonhomogeneousUndeterminedCoefficients
   :members:

nth_algebraic

.. autoclass:: sympy.solvers.ode.single::NthAlgebraic
   :members:

nth_order_reducible

.. autoclass:: sympy.solvers.ode.ode::NthOrderReducible
   :members:

separable

.. autoclass:: sympy.solvers.ode.single::Separable
   :members:

almost_linear

.. autoclass:: sympy.solvers.ode.single::AlmostLinear
   :members:

linear_coefficients

.. autoclass:: sympy.solvers.ode.single::LinearCoefficients
   :members:

separable_reduced

.. autoclass:: sympy.solvers.ode.single::SeparableReduced
   :members:

lie_group

.. autoclass:: sympy.solvers.ode.ode::LieGroup
   :members:

2nd_hypergeometric

.. autoclass:: sympy.solvers.ode.single::Hypergeometric2nd
   :members:

1st_power_series

.. autofunction:: sympy.solvers.ode.ode::ode_1st_power_series

2nd_power_series_ordinary

.. autofunction:: sympy.solvers.ode.ode::ode_2nd_power_series_ordinary

2nd_power_series_regular

.. autofunction:: sympy.solvers.ode.ode::ode_2nd_power_series_regular

Lie heuristics

These functions are intended for internal use of the Lie Group Solver. Nonetheless, they contain useful information in their docstrings on the algorithms implemented for the various heuristics.

abaco1_simple

.. autofunction:: sympy.solvers.ode.lie_group::lie_heuristic_abaco1_simple

abaco1_product

.. autofunction:: sympy.solvers.ode.lie_group::lie_heuristic_abaco1_product

bivariate

.. autofunction:: sympy.solvers.ode.lie_group::lie_heuristic_bivariate

chi

.. autofunction:: sympy.solvers.ode.lie_group::lie_heuristic_chi

abaco2_similar

.. autofunction:: sympy.solvers.ode.lie_group::lie_heuristic_abaco2_similar

function_sum

.. autofunction:: sympy.solvers.ode.lie_group::lie_heuristic_function_sum

abaco2_unique_unknown

.. autofunction:: sympy.solvers.ode.lie_group::lie_heuristic_abaco2_unique_unknown

abaco2_unique_general

.. autofunction:: sympy.solvers.ode.lie_group::lie_heuristic_abaco2_unique_general

linear

.. autofunction:: sympy.solvers.ode.lie_group::lie_heuristic_linear

System of ODEs

These functions are intended for internal use by :py:meth:`~sympy.solvers.ode.dsolve` for system of differential equations.

Linear, 2 equations, Order 1, Type 6

.. autofunction:: sympy.solvers.ode.ode::_linear_2eq_order1_type6

Linear, 2 equations, Order 1, Type 7

.. autofunction:: sympy.solvers.ode.ode::_linear_2eq_order1_type7

Linear ODE to matrix

.. autofunction:: sympy.solvers.ode.systems::linear_ode_to_matrix

Canonical Equations Converter

.. autofunction:: sympy.solvers.ode.systems::canonical_odes

LinODESolve Systems Information

.. autofunction:: sympy.solvers.ode.systems::linodesolve_type

Matrix Exponential Jordan Form

.. autofunction:: sympy.solvers.ode.systems::matrix_exp_jordan_form

Matrix Exponential

.. autofunction:: sympy.solvers.ode.systems::matrix_exp

Linear, n equations, Order 1 Solver

.. autofunction:: sympy.solvers.ode.systems::linodesolve

Nonlinear, 2 equations, Order 1, Type 1

.. autofunction:: sympy.solvers.ode.ode::_nonlinear_2eq_order1_type1

Nonlinear, 2 equations, Order 1, Type 2

.. autofunction:: sympy.solvers.ode.ode::_nonlinear_2eq_order1_type2

Nonlinear, 2 equations, Order 1, Type 3

.. autofunction:: sympy.solvers.ode.ode::_nonlinear_2eq_order1_type3

Nonlinear, 2 equations, Order 1, Type 4

.. autofunction:: sympy.solvers.ode.ode::_nonlinear_2eq_order1_type4

Nonlinear, 2 equations, Order 1, Type 5

.. autofunction:: sympy.solvers.ode.ode::_nonlinear_2eq_order1_type5

Nonlinear, 3 equations, Order 1, Type 1

.. autofunction:: sympy.solvers.ode.ode::_nonlinear_3eq_order1_type1

Nonlinear, 3 equations, Order 1, Type 2

.. autofunction:: sympy.solvers.ode.ode::_nonlinear_3eq_order1_type2

Nonlinear, 3 equations, Order 1, Type 3

.. autofunction:: sympy.solvers.ode.ode::_nonlinear_3eq_order1_type3

Nonlinear, 3 equations, Order 1, Type 4

.. autofunction:: sympy.solvers.ode.ode::_nonlinear_3eq_order1_type4

Nonlinear, 3 equations, Order 1, Type 5

.. autofunction:: sympy.solvers.ode.ode::_nonlinear_3eq_order1_type5

Information on the ode module

.. automodule:: sympy.solvers.ode.ode

Internal functions

These functions are not intended for end-user use.

.. autofunction:: sympy.solvers.ode.ode::_handle_Integral