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Solution behaviour near singular point

  1. May 29, 2012 #1
    1. The problem statement, all variables and given/known data
    Determine the two singular points of the differential equation
    (x2−16)y+(4−x)y+(x2+8x+16)y=0​
    1) List the points in increasing order
    2) Which of the followings describes the behaviour of the solutions of the differential equation near each singular point.
    a)all solutions are bounded
    b)all solutions are unbounded
    c)at least one solution is bounded and at least one solution is unbounded)

    3. The attempt at a solution
    I found out that the two singluar points are: r1 = -4 and r2 = 4 but do not know how to solve 2).

    Thanks in advance!
     
  2. jcsd
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