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The use of information technology in addition to traditional lectures affords a means to develop student intuition and curiosity, reaching in the same time a deep knowledge of the subject of study. The aim of this work is to show the didactic use of a Computer Algebra System to illustrate and compare different symbolic-numerical methods for solving first order ordinary differential equations (ODEs). In particular, we apply, relate and compare the built-in functions of Mathematica, the method of integration by series, the Picard process and the linearization method in solving some first order ODEs. This approach allows students not only to master the basic methods for solving ODEs, but also to be naturally led to theoretical deepening of such areas as power series, stability and convergence theory, elements of functional analysis or the local-global relationship via linearization.
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