# Math 2250
# Fall 2000 Project 1
# Answer Template
# 
#      You should download this template from
# http://www.math.utah.edu/~korevaar/2250proj1ans.txt, and open it from
# Maple as a Maple Text document.  If you are using Matlab rather than
# Maple to do this project, make sure to answer each question that is
# asked here, using Matlab commands where necessary and by creating your
# own answer document.
# 
# 1)  Type in  your name and student number here:
# 
# 
#      You are to complete the Investigation on page 44 of the text,
# from section 1.4.  We have added several additional questions.  It
# would be a good idea to do your project on this template.  If you were
# already working on another Maple file (e.g. the hints file), it would
# be a good idea to restart and to reload DEtools, so that Maple will
# reinitialize everything:
# 
> restart:with(DEtools): 
# 
# (a1)  What value of a=m/n and b=1/n are you taking?
# 
# (a2)  Insert  the plot containing the direction field and solution
# curves here.  Of course, the plot should be preceeded by the Maple
# command(s) which generated it.
# 
> 
# 
# (a3)  What happens to the populations as t goes to infinity?  Explain.
# 
# (b1)  Use the computer algebra system to solve the inital value
# problem for your differential equation symbolically, with x(0)=x0. 
# That is, have the computer do the steps in separating variables,
# integrating, finding the constant of integration in terms of the
# initial values, and finally solving for x as a function of t.
# 
> 
# 
# (b2)  Use "dsolve" to find the solution.  Verify (and explain) why the
# "dsolve" solution agrees with  your answer from (b1).
# 
> 
# 
# (b3)  Work out the solution to the initial value problem of (b1) by
# hand.  You may use Maple to do the partial fractions step, or you may
# do it by hand.  Staple your hand-solution to your final version of
# your Maple answers, and then hand both in together. 
# 
# (c1) State an interesting  numerical problem which could be solved
# from your symbolic solution.  For instance, how long does it take x to
# grow from a selected initial value x0 to a given target value x1?
# 
# (c2)  Solve the problem, using Maple.
>