The singular point analysis of third-order ordinary differential equations in the nonpolynomial class are presented. Some new third order ordinary differential equations which pass the Painlevé test as well as the known ones are found.

2 Separation of variables and the complete integral 5 2.1 Separation of variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 The envelope of a family of curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.3 The complete integral . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.4 Determining the characteristic strips from t...

This study introduced real life application of first order differential equation. In this paper We basically discussed about different types equation and the solution in field science technology. Further, Newton’s law cooling orthogonal trajectory has been incorporated. Study convective boundary condition it is used for increasing temperature.

Using geometric methods for linearizing systems of second order cubically semi-linear ordinary differential equations and third order quintically semi-linear ordinary differential equations, we extend to the fourth order by differentiating the third order equation. This yields criteria for linearizability of a class of fourth order semi-linear ordinary differential equations, which have not bee...

We study the implicit second order ordinary differential equations with complete integral. In this paper, we give a characterization of the implicit second order ordinary differential equations with smooth complete integral which we call Clairaut type equations. Besides, we consider properties of the Clairaut type equations and present the duality among special completely integrable equations w...