Covered today: 2.1 through 2.4. Review of first order linear and separable equations. Also, we briefly touch on the existence and uniqueness theorems (2.2.1 and 2.4.1).

For next time: 2.1 - 13,15,22 and 2.2 - 4,9,16 and 2.3 12,17 and 2.5 - 16. If you haven't already, you should get used to drawing slope fields and solution curves on Maple (although I won't formally assign anything). Here are the Maple commands from class today:

• Remember to enter with(DEtools); to invoke the differential equations package.

• Don't forget to put a semicolon at the end of each command!

• To get the slope field for $y'=\frac{1}{2}y + 2\cos(x)$, enter DEplot(diff(y(x),x) = y/2 + 2*cos(x), y(x), x=-10..10, y = -10..10);

• To get sketches of particular solutions, enter the initial conidtions between x=-10..10 and y=-10..10. For example: try DEplot(diff(y(x),x) = y/2 + 2*cos(x), y(x), x=-10..10, [[y(0)=-2], [y(0)=-1], y = -2..2);

• For help with any command, type ?command. For example ?DEplot would call the help page for the DEplot command.