Abstract
The general properties of the solution of a homogeneous equation are given. Solutions of a homogeneous linear ordinary differential equation of the second order with constant coefficients in three cases related to the coefficients of the equation are investigated. The obtained results are justified in the form of a theorem. These conclusions are proved in the framework of the methods of high school mathematics. This theory, known in general mathematics, is fully adapted to the implementation in secondary school mathematics and developed with the help of new elementary techniques that are understandable to the student. The main purpose of the work was to develop methods for solving a linear homogeneous differential equation of the second-order at a level that a schoolboy can master. The result will be the creation of a special course program on the basics of ordinary differential equations in secondary schools of the natural-mathematical direction, the preparation of appropriate content material, and providing them with a simple teaching method.
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