Name ______________________________________   UTEID_____________

Homework 4  Math 427K   Uhlenbeck  Due  February 24, 2005

Please give your answers on this sheet and staple your worksheets
to the back of this page.

1.  Find the general solution to the equation


     y"  +  11y' +  30 y  =   0.









2.  Find the solution to  y" -  9y  =  0  with y(0) = 0 and y'(0) = 1.









3. Consider the equation y"  +  t^(-1)y'  -  t^(-2)y = 0.  Verify that
y= t and y= t^-1  are both solutions to the equation.  Give the 
general  solution to the equation and find the solution with y(1) = 0
and y'(1) = 1.











4.  Find all real solutions to the equation y" + 2y' + 10y =  0.  









5.  Find the general  real  solution to  y" -2y'  +  2y  = exp(3t) + 2.