Physical Sciences and Mathematics Commons^™

The Existence Theorem Of Ordinary Differential Equations, Harris J. Dark

Master's Theses

There are a great many devices for solving differential equations of certain special forms. But there is a large number of classes of differential equations that are not included in these special forms and cannot be integrated by quadratures or other purely elementary methods. When mathematicians were forced to abandon their cherished hope of finding a method for expressing the solution of every differential equation in terms of a finite number of known functions or their integrals they turned their attention to the question of whether a differential equation in general had a solution at all, and, if so, of …