Volume no :1, Issue no: 1, April 2008

Journal of Mathematical Sciences: Advances and Applications

ANALYTICAL CLOSED FORM AND APPROXIMATE SOLUTIONS FOR QUADRATIC NONLINEAR FIRST ORDER ODEs

Author's: M. P. Markakis
Pages: [153] - [165]
Received Date: March 26, 2008
Submitted by:

Abstract

By using appropriate transformations, a “quadratic” non-homogeneous first order nonlinear ordinary differential equation is reduced to an Abel equation of the first kind, where the “hyperbolic” structure of the analysis allows in some cases the derivation of closed form solutions, while in most cases, analytical approximate solutions can be extracted within certain domains.

Keywords

nonlinear ODEs, analytical methods, closed form solutions, approximate solutions.