Generalized Bernoulli equation as a source for generating tasks of increased complexity

Abstract

The technology of creating problems of increased complexity based on generalized ordinary differential equations of Bernoulli is considered. Such problems contribute to the development of mathematical abilities of students, stimulate them to creative search, develop abstract thinking and ingenuity. It is emphasized that when developing such problems it is important to maintain a balance between complexity and accessibility. It is described how the generalized Bernoulli equation can be transformed into a linear equation using the appropriate substitution. An example of solving such an equation is shown. A promising direction of further research is the creation of an interactive application for generating problems based on the generalized Bernoulli equation.