M 427K (Spring 2007)
Problem Set 2
Due: Thursday, February 8, 2007 1
Problems from Textbook
Section Problem(s)
2.1 31, 38, 39
2.2 8, 30(a – e)
2.3 8(b,c), 16, 23(a – d), 27
For 2.3.23, use the convention that positive direction for position is upward, and use the following approximate value
for the acceleration due to gravity: g≈32.174 ft/s2. Note also that the weight of an object is equal to the product of
its mass and the (universal) acceleration due to gravity.
Maple Question
1. a) Problem 23(e), Section 2.3. Plot over the time interval [0,30]. Use the convention that positive direction (for
position, hence for velocity as well) is upward.
(Hint: Look up the Maple function piecewise( ).)
b) Plot also the position function over the time interval [0,30]. Use the same convention of direction.
2. Consider Problem 5 of Section 2.2.
a) Solve the differential equation using dsolve( ).
b) Solve the differential equation using dsolve( · · · ,implicit).
c) Use implicitplot( ) to plot the solution curves with the following initial conditions:
y(0) = 1
2arctan 2i
5, i =−5, . . . , 5.
Make your plot over this viewing area: x, y ∈[−5,5] ×[−0.75,0.75]. Make sure the curves in your plot “look”
smooth.
d) Use DEplot( ) to plot the direction field and the solution curves with the following initial conditions:
y(0) = i
10, i =−6, . . . , 6.
Make your plot over this viewing area: x, y ∈[−5,5] ×[−0.75,0.75]. Make sure the curves in your plot “look”
smooth.