Integrating linear ordinary fourth-order differential equations in the MAPLE programming environment

This paper reports a method to solve ordinary fourth-order differential equations in the form of power series and, for case regular special points, generalized series. An algorithm has been constructed and program developed MAPLE environment (Waterloo, Ontario, Canada) order equations. All types solutions depending on roots governing equation have considered. The examples are given; they compared with results available literature that demonstrate excellent agreement calculations reported here, which confirms effectiveness programs. A feature this work is accuracy controlled by number terms symbols (up 20) decimal mantissa numerical calculations. Therefore, almost any allowed given electronic computing machine or computer achievable. proposed symbolic-numerical could be successfully used solving eigenvalue problems, very important as eigenfunctions extremely (exponentially) sensitive eigenvalues found. implemented other known algebra packages such REDUCE (Santa Monica, CA), MATHEMATICA (USA), MAXIMA others. construct Green’s functions boundary private derivatives, system Hamilton’s equations, problems related mathematical physics.