Name________________________________   UTEID_______


Math 427k        Uhlenbeck       Homework 7    Due March 31, 2005

Please write your answers on this page and staple your worksheets
and computer output to the back.

             1 1 2
1.  Let A =  1 2 1.  You are told that A has eigenvalues -1, 1, 4. Find
             2 1 1

the general solution to the equation x' = A x.
  







2.  Let x' = -2x + 3y;  y' = x - 4y.  Find the general solution to

this system of equations.







3.  Solve the system of equations in problem 2 with the initial data

x(0) = 1, y(0) = 3.









4.  Find the general real solution to the equation  x' = 2x -5y; y'= 4x - 2y.












5.  Use pplane to graph the direction field for the system in problem 2
and problem 4. Graph on each direction field the solution with x(0)= 1, 
y(0) = 3.