# PureAlgebraicLODE(F, UP, UPUP, R)¶

In-field solution of an linear ordinary differential equation, pure algebraic case.

algDsolve: (LinearOrdinaryDifferentialOperator1 R, List R) -> Record(particular: List Record(ratpart: R, coeffs: Vector F), basis: List R)

algDsolve(op, lg) is a parametric version of algDsolve(op, g)

algDsolve: (LinearOrdinaryDifferentialOperator1 R, R) -> Record(particular: Union(R, failed), basis: List R)

algDsolve(op, g) returns ["failed", []] if the equation op y = g has no solution in R. Otherwise, it returns [f, [y1, ..., ym]] where f is a particular rational solution and the y_i's form a basis for the solutions in R of the homogeneous equation.