Third graded homework (due 10/27)

For maximal credit, full working must be shown.
  1. (3 points.) Write the function
    u(t) = 4 cos t - 3 sin t
    in amplitude-phase form.

  2. (4 points.) Find a particular solution to the differential equation
    y'' + y = csc t
    for initial data at  t = 1.

  3. (4 points.) Give the general solution to the differential equation    
    t2y'' - 3ty' + 4y = 0
    in the range  t  >  0. If you wish, you may assume that
    y1(t) = t2
    is one solution.