find the general solution using computer software (such as, Mathematica, MATLAB, or Maple).
In each case find the general solution, both using the “off-the-shelf” formula (21) and then again by actually carrying out the steps of the integrating factor method. That is, find the integrating factor σ(x) and then carry out solution steps analogous to those in our derivation of (21). Understand the x interval on which the equation is defined to be the broadest interval on which both p(x) and q(x) are continuous. For example, in part (a) the x interval is − ∞ < x < ∞, in part (e) it is any interval on which tana; is continuous (such as π/2 < x < 3π/2), and in part (f) it is either − ∞ < x < 0 or 0 < x < ∞ [to ensure the continuity of p(x) = 2/x].
y′ − y = 3ex
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