Name________________________________   UTEID_______


Math 427k        Uhlenbeck       Homework 5    Due March 3, 2005

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

1.  Find the general solution to the equation

        y"' +  y" + y' + y =  t^2 + 3.






2. Find the solution of the equation    y" + 4y' = 2 sin(3t)

   with y(0) = y'(0) = 0.







3. Find all the  6th roots of  -27. 







4.  Rewrite the equation  y" +.5y' + 2y = 4 as a system of two equations
in y and y' = x.   Use the matlab program pplane, which is very similiar
to dfield, to graph the solution curve in the plane (x(t), y(t) with
(x(0) = 0, y(0) = 0).   Graph another solution with (x(0) = 1, y(0) = 1).
What happens to the solutions as t goes to infinity? Now graph the
solutions to the overdampened problem y" + 3y' + 2y = 4 with the same
initial data.  Describe the difference.












5 Use dsolve (a program in matlab) or another symbolic manipulator
program  to find the   solutions of y" - 4y' + 17 y = cos t with
y(0) = y'(0) = 0. (You might want   to check your other solutions with
the same program).