Differential Equations is an important field of research in Mathematics, both for its mathematical rigor and for its multiplicity of applications in various scientific fields, such as Physics, Biology and Engineering. In all these areas of knowledge we are faced with phenomena modeled from differential equations, this fact justifies the importance of its study over the last three centuries. In the present work, we will investigate the existence of a solution to a eigenvalue problem on the line involving a differential equation with boundary values. The idea is to find all the values for which the solution to the problem is non-trivial, called eigenvalues, and the eigenfunctions associated with these eigenvalues. This problem relates differential equations with concepts of Linear Algebra and Differential and Integral Calculus, in addition, it is included in a large class of boundary value problems, called Sturm-Liouville Problems, which has properties relevant to its study.
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