ABOUT THE FORM OF THE SOLUTION OF A THIRD-DEGREE EQUATION WITH FUNCTIONAL COEFFICIENTS

Abstract

In this work we discuss the following linear differential equation of third degree

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

and we transform it under certain circumstances in its canonical form (1) whereupon

\(a(x)=c,\)

which is a differential equation with constant coefficients, and according to the sign of the figuration equations we determine its solution with the formulas (2).