How do you plot solutions of an O.D.E?

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One advantage of using technology is that often when a large number of problems are solved, their solutions are compared and conjectures about general patterns can be dis- covered and tested. Sage is capable of solving a variety of O.D.E’s. Use Sage to construct a conjecture about the following:

(a) Compare the solutions of dy/dx + y = f(x) subject to y(0) = 0, where f(x) = x, sin x, cos(x), and ex.

(b) Compare the solutions of dy/dx + y = x subject to y(0) = k, where k = −2, −1, 0, 1, 0, 1, 2