International Journal of Mathematics and Mathematical Sciences
Volume 1 (1978), Issue 3, Pages 257-267

Nonlinear differential equations and algebraic systems

Lloyd K. Williams

Department of Mathematics, Texas Southern University, Houston 77004, Texas, USA

Received 17 April 1978

Copyright © 1978 Lloyd K. Williams. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In this paper we obtain the general solution of scalar, first-order differential equations. The method is variation of parameters with asymptotic series and the theory of partial differential equations.

The result gives us a form like a differential quotient requiring only that a limit be taken. Like the familiar expression for the solution of linear, first order, ordinary equations, it is the same in all cases.