Kovacic(F, UP)

kovacic.spad line 1 [edit on github]

• F: Join(CharacteristicZero, AlgebraicallyClosedField, RetractableTo Integer, RetractableTo Fraction Integer)

• UP: UnivariatePolynomialCategory F

Kovacic provides a modified Kovacic's algorithm for solving explicitly irreducible 2nd order linear ordinary differential equations.

kovacic: (Fraction UP, Fraction UP, Fraction UP) -> Union(SparseUnivariatePolynomial Fraction UP, failed)

kovacic(a_0,a_1,a_2) returns either “failed” or P(u) such that \$e^{\int(-a_1/2a_2)} e^{\int u}\$ is a solution of a_2 y'' + a_1 y' + a0 y = 0 whenever u is a solution of P u = 0. The equation must be already irreducible over the rational functions.

kovacic: (Fraction UP, Fraction UP, Fraction UP, UP -> Factored UP) -> Union(SparseUnivariatePolynomial Fraction UP, failed)

kovacic(a_0,a_1,a_2,ezfactor) returns either “failed” or P(u) such that \$e^{\int(-a_1/2a_2)} e^{\int u}\$ is a solution of \$a_2 y'' + a_1 y' + a0 y = 0\$ whenever u is a solution of P u = 0. The equation must be already irreducible over the rational functions. Argument ezfactor is a factorisation in UP, not necessarily into irreducibles.