Problems, Solutions of which Lead to a Differential Equation

Key words: equation type, solution method, independent and dependent variables, substance density, exponential growth, initial condition The paper considers a number of problems related to various fields, for the solution of which differential equations are widely used. Based on the laws of a given field, the corresponding differential equations are compiled. The main goal of the researcher should obtain an equation of the functional dependence between the variable parameters of a given process. Most of such equations are reduced to a differential equation that contains derivatives or differentials of an unknown function. To solve this equation means to obtain an equation that does not contain derivatives and differentials, from which this equation follows as a consequence. When solving problems related to the compilation of differential equations, the geometric and physical meaning of the derivative, as well as the known laws of natural and social sciences, are widely used. The formulation of a differential equation that meets the conditions of a scientific or technical problem means deciding which of the variables in the problem should be considered an independent variable, and which one should be considered a dependent variable, and then finding a mathematical relationship between the variables and their increments. The solution of the resulting differential equation is an important, but purely technical problem.