Solving Homogeneous Linear Differential Equations in Terms of Second Order Linear Differential Equations

DOI10.2307/2374373zbMath0564.12022OpenAlexW2319797753MaRDI QIDQ3677847

Michael F. Singer

Publication date: 1985

Published in: American Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2374373

zbMATH Keywords

linear differential operatorsMathieu's equationdifferential fieldMACSYMAhomogeneous linear differential equationGalois theory of differential fieldsthird order homogeneous linear differential equationsREDUCE-2connected Galois groupeulerian solution

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Linear differential equations in abstract spaces (34G10) Differential algebra (12H05) Abstract differential equations (12H20)

Related Items (21)

An algorithm for solving second order linear homogeneous differential equations ⋮ Absolute reducibility of differential operators and Galois groups ⋮ Descent for differential modules and skew fields ⋮ Necessary conditions for Liouvillian solutions of (third order) linear differential equations ⋮ A characterization of reduced forms of linear differential systems ⋮ Faà di Bruno's formula and modular forms ⋮ Computer algebra: Past and future ⋮ Radial basis function methods for the Rosenau equation and other higher order PDEs ⋮ Differential and difference algebra ⋮ On the solutions of holonomic third-order linear irreducible differential equations in terms of hypergeometric functions ⋮ Painlevé equations, integrable systems and the stabilizer set of Virasoro orbit ⋮ Closed form solutions of linear difference equations in terms of symmetric products ⋮ Stieltjes moment sequences for pattern-avoiding permutations ⋮ Liouvillian solutions of third order differential equations ⋮ On the Solutions of Holonomic Third-Order Linear Irreducible Differential Equations in Terms of Hypergeometric Functions ⋮ On Liouvillian solutions of linear differential equations ⋮ On \(d\)-solvability for linear differential equations ⋮ Some remarks concerning them-reduction of differential equations ⋮ Formal solutions of differential equations ⋮ Level crossings and new exact solutions of the two-photon Rabi model ⋮ Galois properties of linear differential equations

Uses Software

• REDUCE
• MACSYMA

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