POWER SERIES METHOD IN SOLVING DIFFERENTIAL EQUATIONS IN THE OSCILLATION BRANCH IN PHYSICS

The differential equations appear with many frequencies in the studies of the physical phenomena, as in the rocks present in the branch of the classic mechanics, in the quantum and in the electromagnetism. In particular, there are a wide variety of keys of their equations that are 2nd order variables, especially with constants, be they ordinary or partial. The purpose of this work is the resolution of some differential equations that appear in Physical-Mathematical problems, using the Power Series method, emphasizing Theoretical Physics, aiming at mathematics as a tool of physics and showing its rigor. For this, it is necessary to use certain methods, properties or axioms. Differential equations are many found in physical problems such as: The wave equation, which led to the invention of radio, radar, television and wireless connections; In mechanics, as oscillations: damped oscillations, forced oscillations, simple harmonic motion, the spring mass system, the mathematical pendulum; In electricity, the RL system, in thermodynamics, the heat equation and so on. It is important to emphasize that these problems can be solved by other methods, because mathematics offers us many avenues and in this way, the physical understanding will be established.