Advanced Engineering Mathematics, 7th Edition

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.

1. The general solution of x² y″ + xy′ + (x² − 1)y = 0 is y = c₁J₁(x) + c₂J₋₁(x). _______
2. Since x = 0 is an irregular singular point of x³y″ − xy′ + y = 0, the DE possesses no solution that is analytic at x = 0. _______
3. 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]

4. x = 0 is an ordinary point of a certain linear differential ...