Math 306B                   Math Lab #5

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DUE 3/1/04 (Mon.)

Problem #1: (Read: Text #2: Chap. 13, pp. 171 -177) .

(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 .

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DUE 3/8/03 (Mon.)

Problem #2: (Read pp. 165-168 of Text #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).

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

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

C.O. Bloom