The methodological manual is written according to the program on differential equations for the specialty "Mathematics and computer science". The methodical manual includes only first order differential equations. The manual first provides theoretical material, which is necessary for a specialist in his practical activity. The solution of different differential equations of the first order is considered. The material is presented in an accessible way, detailed conclusions are given. Examples accompanied by detailed solutions are included. At the end there are examples for an independent solution, and after each topic, examples for an independent solution are given.This book has been translated with Artificial Intelligence.