Problem 1.   Boas Problems #5 & #6, Ch.12.20, page 604.

Problem 2.   Boas Problems #13 & #15, Ch.12.20, page 605.

Problem 3.   Boas Problem #12, Ch.12.21, page 606. (Hint: Plug the two proposed solutions into the given differential equation and show they both solve it (to give zero) by taking the solutions' derivatives carefully with the chain rule. Then expand these two solutions in a Taylor series around 1/x (which you get by just taking the series for sine and cosine with x replaced with 1/x) and show that these two solutions do not have the form of a Frobenius series, which is given in Eq.11.1, by eyeballing it. You will see that instead of just one or two terms with powers of x in the denominator you will have an infinite number of terms with ever increasing powers of x in the denominator. This is called an isolated essential singularity and is not of the Frobenius type.

Problem 4.   Boas Problem #5, Ch.12.22, page 612.

Problem 5.   Boas Problem #6, Ch.12.22, page 612.