Homework Assignment Two, Math 366, Wilkerson Section
Due Sept. 5, 2001 before 4PM


1. Use the existence and uniqueness theorem for first order linear
   equations to show that if y(t) is a solution to
   y' -ky = 0 with y(0) = 1, then
   y(a+b) = y(a)y(b) for all real numbers a and b. DO NOT
   ASSUME that y(t) = exp(kt)!

   Hint: Let x(t) = y(a)y(t). What is x'(t)?
   Comment: all the usual properties of exponential functions
   can be derived from the DE above.

2. A meteor crashes into the Wabash at midnight. A diver at 6AM
   is unable to handle it because of the heat.  Its temperature
   at that point is 200 degrees F. At 12 noon, the temperature has
   decreased to 150 degrees F. Use the ODE for Newton's law of
   cooling ( page 75) to estimate temperature of the meteor at the 
   time of impact. Assume that the water temperature of the Wabash is 
   a constant 75 degrees F.

Homework from the textbook:

Page 65   3,4
Page 78   10,13,21, 22
Page 84   19,20
Page 92   2,3,11