4.2 11, 13, 32, 33, 37.

5.1 is review. No required problems.

5.3 2, 3, 4, 5, 7.

"5.2": For #1-3 below find the general series solution. That is, find a recursive formula for a_n, so that if we know a₀ and a₁, we could find as many terms as we wanted.

1. y'' - y = 0; centered about x=0.

2. y'' - y = 0; centered about x=1.

3. y'' + 2xy' - y = 0; centered about x=1.

For #4 do the following: (a) Find the general series solution as above.
(b) Find the first five terms when y(0)=1 & y'(0)=0. Call this solution y₁.
(c) Find the first five terms when y(0)=0 & y'(0)=1. Call this solution y₂.
(d) Explain why y₁ and y₂ must be linearly independent.

4. 2y'' + xy' + 3y = 0; centered about x=0.

5. Redo the #4 (b) & (c) with a computer, but find the first 10 terms.