In the Comment at the end of Example6we wondered what the divergence of the series solution over 7 < x < ∞implied about the nature of the solution over that part of the domain. To.gain insight, we propose studying a simple problem with similar features. Specifically, consider the problem
(x−1)y′ +y = 0, y(4) = 5 (12.1)
on the interval 4 ≤x < ∞.
Solve (12.1) analytically, and show that the solution is
over 4 ≤ x < <<<∞. Sketch the graph of (12.2), showing it as a solid curve over the domain 4 ≤ x < ∞ , and dotted over − ∞ < x < 4.
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