__Math 306T__**
Math Lab #5 **

**Read: **Text #2: Chap. 13, pp. 171 -177 .

**-------------------------------------------------------------------------------------------**

**Submit the following two problems for
grading :**

**Problem #1:**

**(a)**-[2 pts.] Use the Maple command **dfieldplot **in the** DEtools **package
to plot the direction field for the following linear, first order system: y' = v, v' = -2y - v. (See p.194 of Text #2)

**(b)**-[4 pts.] Use the Maple command **DEplot** in the** DEtools **package
to construct a phase portrait for the given system.

To accomplish this use the Maple command **DEplot**
with the following initial conditions:

[y(0),v(0)] = [0,-2], [y(0),v(0)] = [0,1], [y(0),v(0)] = [0,2], [y(0),v(0)] = [0,3], [y(0),v(0)] = [0,4].

**(c)**-[2 pts. ] Let [y(t), v(t)] be the solution of the given system that
satisfies the initial condition [y(0),v(0)] = [0,1]. Use the Maple command **DEplot**
with the option **scene=[t, y] **to graph y(t) for 0 £ t £ 10 (See bottom of p.169 of
Text #2). Use the command **DEplot** with the option **scene=[t,v] **to
graph v(t) for 0 £ t £ 10.** **(See bottom of
p.169 of Text #2).

**(d)**-[2 pts.] Use the results of **(c)** and the **display **command**
**in the** plots **package** **to plot y(t) and v(t) on the same graph
.

___________________________________________________________________________

**Problem #2:**

**(a)**-[5 pts.] Use the Maple command **dsolve **to find the solution of
first order, linear system y' = v, v' = -2y - v that satisfies the initial conditions y(0) = c,
v(0) = d.

**(b)**-[5 pts.] Plot the solutions corresponding to the initial conditions
given in part **(b)** of Problem #1 using the appropriate **plot**
command (See pg.197 of Text #2), and the command **seq **(See pg.197 of Text
#2).

_______________________________________________________________________________

Text #1= Differential** Equations**
by Blanchard, Devaney and Hall

Text #2= Differential** Equations with
Maple** by Coombes, Hunt, Lipsman, Osborn, Stuck

**C.O. Bloom**