Order of growth of solutions of linear complex differential equations when the coefficients have same order

Abstract

This article contains the theorems which shows that when A(z) = h 1 (z)e P1(z) and B(z) = h 0 (z)e P0(z) are of same order,then all the non-trivial solutions of equation f ′′ + A(z)f ′ + B(z)f = 0 are of infinite order. Moreover we extend these results to higher order differential equations. 2020 Mathematics Subject Classification. 34M10, 30D35. Key words and phrases. entire function, order of growth and complex differential equation.