SOLUTION OF THE CAUSHIE PROBLEM FOR A UNIQUE EQUATION

Abstract

In many important cases, it is convenient to express the simple state of the system at time t by the numerical vector . The rate of change of this vector for time t and itself is as follows

we come to the differential equation. The main issues studied here are the conditions for the existence of a unique solution of the equation for different initial conditions and the conditions for the existence of unique solutions of two or multi-point boundary value problems, changes in the solutions of linear equations with constant and variable coefficients, linear and nonlinear equations stability of decisions.

By analyzing this simple equation, as a result of painstaking and deep research, we can obtain many important data about physical phenomena. However, some phenomena in nature force us to consider more complex equations than before.