Ratios and proportions are rudimentary notions, but extremely important and with many implications in understanding of other more advanced notions in mathematics. In this article, via examples of solved problems, we show ...

Consider the general cubic differential system x & = P(x, y), y & = Q(x, y) , where P Q x y , , E [ ], max deg ,deg 3 { P Q} = ,GCD P Q ( , 1 ) = . According to [1], a differential system is Darboux integrable if this ...