Solving second-order ordinary differential equations without using complex numbers

Ordinary differential equations (ODEs) is a subject with a wide range of applications and the need of introducing it to students often arises in the last year of high school, as well as in the early stages of tertiary education. The usual methods of solving second-order ODEs with constant coefficients, among others, rely upon the use of complex variable analysis, a topic to which the students in question may not have been previously introduced. The purpose of this article is to present an alternative approach in establishing the general solution for such types of equations without using complex numbers.