Homework 2

  Use matlab or maple to find general solutions to the following
equations.  You will need to use the computer to find the roots of the
indicial equations. I have not yet figured out how to do this on
maxima or octave.



  Then plot a sample solution using netmath (octave) (look under higher order
differential equations for instructions and samples  ).  You may also use
 mathlab or maple to do this  if you like. It is your choice.

1. y''' - 3 y' + y = 0.

2. y''' + 3y'' - 3y = 0.

3. y''' + y' + y = 0.

4. y''' + 3y' +5 y = 0.

5. y'''' + 2y''' - 3y = 0.

6. y'''' + 3 y' - 4y = 0.


You cannot plot the direction fields in dfplot.  This only works for
second order systems.  You will have to use octave.


To use matlab from the mathematics department computer, type matlab
at the prompt.  To find the roots of the first example, type at the
mathlab prompt

roots ([1 O -3 1])


To use maple, type   maple   at the math department prompt.  At the maple
prompt type


     fsolve(r^3 - 3*r + 1 = 0);


While you are there, take a look at the other things these programs
can do for your math skills!


To use ODE solver on netmath, you will have to convert these equations
to  systems.  The first equation will have three variables.

  xdot(1)  = x(2)
  xdot(2)  = x(3)
  xdot(3) =  3*x(2) - x(1).


Now comes the hard part.  Suppose you want to print only the solution.
In other words, you do not want the beautiful colored graphs of x(2)
and x(3) coming along with x(1).  Replace the plot command by

     plot(t,[sol (:,1)'])

The ,"@" is added if you want to see the dots.  To thinken the lines
so they print correctly, go over to config and change the line wide to
something more like 2 instead of .6.

And so forth.

Have fun.  Itis important to learn to use the computer to do the calculations
so your brain will be free for thinking!