We introduce a method for finding general solutions of third-order nonlinear differential equations by extending the modified Prelle-Singer method. We describe a procedure to deduce all the integrals ...

The deterministic factorization algorithm for polynomials over finite fields that was recently introduced by the author is based on a new type of linearization of the factorization problem. The main ...

Mathematicians finally understand the behavior of an important class of differential equations that describe everything from water pressure to oxygen levels in human tissues.

We all know how differential equations are a crucial part of engineering design and analysis. We have some powerful software tools for this today. Well, here is what led up to our modern analysis ...