Covered today: We will solve some simple DEs using series, and this will lead to the notion of representing functions with series.

For next time: 2.2 - 13,21,22,24. Also, Obtain a series solution for each of the following differential equations. If possible, find the general term in each solution. If not, find the first eight terms:

1.

y'-4y=0

2.

ty'+2y=t²-t+1

3.

y'' - 3y = 0

4.

(1-x)²y' = 1

Maple commands used in class today:

• plot(t, t=-10..10, y=-10..10);

• plot([t, t-t^3/6], t=-10..10, y=-10..10);

• plot([t, t-t^3/6, t-t^3/6 + t^5/5!], t=-10..10, y=-10..10);

  etc.