Math 3200 Differential Equations Homework # 1 Due Jan 24,2000 8:15AM Lyndell Kerley, PhD

DIRECTIONS: DON'T WRITE ON THE BACK OF THE PAPER. STAPLE IN ORDER ASSIGNED.

Use command t in MDEP to write a description on each plot. Use command t and Ctrl-H (for help) to label a point or 2.

Problem # 1

• Consider the differential equation . Solution will require 4


different plots and supporting discussion. will be written root(2/pi)*cos(x^2) in MDEP.

(a) Use MDEP and Euler technique (nth order DE) to plot the solution for x = 0 to x = 10.



(b) Once (a) is done, press D to overlay with a direction field.

(c) Use MDEP to define and

define . Plot f2.

(d) As stated in problem 2, p 29, calculate the power series expansion via pencil and paper. Define a function f3 = first 3 non-zero terms of the power series expansion. Then plot f3.

Problem # 2

A parachutist is falling with speed 176 ft/sec when his parachute opens. If the air resistance is Wv²/256 lb, where W is the total weight of the man and parachute, find his speed as a function of the time t after the parachute opened. Solution will require 3 different plots and supporting discussion.

The solution begins as

Net force on system = weight of system - air resistance.








(a) Use a table of integrals, Derive, TI92, or some other source to find the exact solution were v = a function of e^-4t.


(b) Find analytically

(c) Use the solution in a. to define f1. Plot f1.


(d) Apply MDEP to (*) above using Euler technique (nth order DE) to exhibit a plot.

(e) From d., press D to exhibit the slope field.

Problem # 3

Consider p11, problem 1e. Find the exact solution. Discuss monotonicity and concavity only.