Supplemental Homework
January 10, 2000

Due January 12, 2000

Solve the following equations using the power series techniques discussed in class: (assume $y=\sum_{j=0}^{\infty} a_j x^j$, solve for the coefficients a_j)

1. y' - 3y = 0.

2. 3xy' + y = x² + x + 1

3. y'' - 4y = 0

4. (1+x)²y' = -1.

If you cannot find an expression for the general term (it may not be possible), then just write out the first six terms of the series.