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Some linear differential equations of second order are analyzed with variable coefficients as well as other nonlinear equations. Some examples are presented to illustrate the deep differences. Next, the form is shown in that the oscillator mass-spring, it can be good to predict some of the qualitative characteristics of more complex equations. This presentation allows professors to integrate the software Mathematica in qualitative analysis, very common in ordinary differential equations. Likewise, it allows the students to visualize the concepts and properties of the differential and integral operators better, as well as provideing the opportunity to carry out numeric experiments and realistic applications.
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