  A series of problems in different fields such as physics and chemistry are
modeled by differential equations. Differential equations are divided into
partial differential equations and ordinary differential equations which can be
linear or nonlinear. One approach to solve those kinds of equations is using
orthogonal functions into spectral methods. In this paper, we firstly describe
Laguerre, Hermite, and Sinc orthogonal functions. Secondly, we select three
interesting problems which are modeled as differential equations over the
interval $[0, +\infty)$. Then, we use the collocation method as a spectral
method for solving those selected problems and compare the performance of
Laguerre, Hermite, and Sinc orthogonal functions in solving those types of
equations.
