5 Chapter in Review Answers to selected odd-numbered problems begin on page ANS-14.
In Problems 1 and 2, answer true or false without referring back to the text.
- The general solution of x2 y″ + xy′ + (x2 − 1)y = 0 is y = c1J1(x) + c2J−1(x). _______
- Since x = 0 is an irregular singular point of x3y″ − xy′ + y = 0, the DE possesses no solution that is analytic at x = 0. _______
- Both power series solutions of y″ + ln(x + 1)y′ + y = 0 centered at the ordinary point x = 0 are guaranteed to converge for all x in which one of the following intervals?
(a) (– ∞, ∞)
(b) (–1, ∞)
(c) [– , ]
(d) [–1, 1]
- x = 0 is an ordinary point of a certain linear differential ...
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