ElementaryFunctionLODESolver(R, F, L)

odeef.spad line 563 [edit on github]

• R: Join(Comparable, PolynomialFactorizationExplicit, 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 = g or “failed” if no non-trivial solution can be found; When found, the solution is returned in the form [h, [b1, ..., bm]] where h is 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; x is the dependent variable.

solve: (L, F, Symbol, F, List F) -> Union(F, failed)

solve(op, g, x, a, [y0, ..., ym]) returns either the solution of the initial value problem op y = g, y(a) = y0, y'(a) = y1, ... or “failed” if the solution cannot be found; x is the dependent variable.