This is part of my 30 years research on Riccati equations and polynomials. We will solve many Riccati differential equations and polynomials, particularly quintic equations, using Riccati equations as DNA of entire mathematics.

Many applications regarding integrations and classical equations of physics are discussed.

This is via the manipulation of “Higher Order Linear Differential Equations.”

New sets of solutions of Bessel equations are presented with trigonometric entities.

It is author’s viewpoint that developments of this research will be an essential part of future research topics in science and technology as well as medicinal sciences.