ON THE SOLUTION AND SOLVING OF LINEAR DIFFERENTIAL EQUATION OF THIRD ORDER WITH FUNCTIONAL COEFFICIENTS

Abstract

A linear differential equation of third order

\(f(x)y''' + g(x)y'' + h(x)y' + r(x)y = 0,\)

is observed in this paper. Under certain conditions it is transformed in the differential equation with constant coefficients of the type (1). Then, according to the sign of the corresponding functions, its solution is obtained, defined by the formulae (2). It can be determined whether it is monotonically increasing or oscillatory.