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Commands for ODEs

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DEtools/singularities
compute the regular and irregular singular points of a homogeneous linear ordinary differential equation (ODE)

DEtools/FunctionDecomposition
perform rational function decomposition on overdetermined systems in the presence of parameters

DEtools/ODEInvariants
computes relative invariants for linear and nonlinear ODEs of order 3 and higher

DEtools/buildsol
build a solution to an ODE using a reduction of order returned by dsolve and a solution to the reduced ODE

DEtools/buildsym
build the symmetry generator given a solution of an ODE

DEtools/canoni
look for a pair of canonical coordinates for a given Lie group of symmetries

convert/ODEs
convert ODEs to other ODEs of different type

DEtools/equinv
look for the most general ODE invariant under a given symmetry

DEtools/eta_k
determines the k-prolongation of the infinitesimals of a one-parameter Lie group

DEtools/firint
calculate first integrals for exact ODEs

DEtools/firtest
test a given first integral

DEtools/gensys
return the determining PDE system for either the coefficients of the symmetry generator or the integrating factor

DEtools/infgen
find the k-extension of the infinitesimal generator of a one-parameter Lie group

DEtools/intfactor
look for integrating factors for a given ODE

DEtools/invariants
calculate the differential invariants of a given one-parameter Lie group

DEtools/line_int
compute F, the solution to Nabla(F) = G, as a line integral when the partial derivatives of F are given

DEtools/muchange
change variables in the integrating factor of an ODE

DEtools/mutest
test a given integrating factor

DEtools/normalG2
calculate the normal form of the generators of a 2-D solvable Lie algebra

DEtools/ode_int_y
given the nth order linear ODE satisfied by y(x), compute the nth order linear ODE satisfied by int(y(x),x)

DEtools/odepde
return the PDE for the coefficients of the symmetry generator

DEtools/power_equivalent
computes an equivalent ODE with invariants with minimal degrees with respect to power transformations

DEtools/redode
return the nth order ODE having a given integrating factor

DEtools/reduce_order
reduce the order of an ODE using symmetries or solutions

DEtools/remove_RootOf
rewrite a given expression removing RootOf.

DEtools/solve_group
represent a Lie Algebra of symmetry generators in terms of derived algebras

DEtools/symgen
look for a symmetry generator for a given ODE

DEtools/symtest
test a given symmetry

DEtools/transinv
look for the set of transformations of variables which leave the ODE invariant

DEtools/Xchange
change variables in an ODE point symmetry generator

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