ElementaryFunctionLODESolver(R, F, L)¶
- R: Join(Comparable, EuclideanDomain, RetractableTo Integer, LinearlyExplicitOver Integer, CharacteristicZero)
- F: Join(AlgebraicallyClosedFunctionSpace R, TranscendentalFunctionCategory, PrimitiveFunctionCategory)
- L: LinearOrdinaryDifferentialOperatorCategory F
ElementaryFunctionLODESolver provides the top-level functions for finding closed form solutions of linear ordinary differential equations and initial value problems.
- solve: (L, F, Symbol) -> Union(Record(particular: F, basis: List F), failed)
solve(op, g, x)returns either a solution of the ordinary differential equation
op y = gor “failed” if no non-trivial solution can be found; When found, the solution is returned in the form
[h, [b1, ..., bm]]where
his a particular solution and and
[b1, ...bm]are linearly independent solutions of the associated homogenuous equation
op y = 0. A full basis for the solutions of the homogenuous equation is not always returned, only the solutions which were found;
xis the dependent variable.