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Math Help - Two short, multiple-choice questions about singular points of a differential equation

  1. #1
    s3a
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    Two short, multiple-choice questions about singular points of a differential equation

    Hello everyone. I am trying to do the following problem (and another one that is similar), but I don't know how to do parts (ii) and (iii), and I was hoping that someone could tell me the thought process that I must have when answering those parts, since I don't even know how to start.Any help would be GREATLY appreciated!
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  2. #2
    s3a
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    Re: Two short, multiple-choice questions about singular points of a differential equa

    ================================================== ==================================================
    Problem & Questions:
    (i) Determine the two singular points x_1 < x_2 of the following differential equation.:
    (x^2 4) y'' + (2 x) y' + (x^2 + 4x + 4) y = 0

    (ii) Which of the following statements correctly describes the behaviour of the differential equation near the singular point x_1?:
    A. All non-zero solutions are unbounded near x_1.
    B. At least one non-zero solution remains bounded near x_1 and at least one solution is unbounded near x_1.
    C. All solutions remain bounded near x_1.

    (iii) Which of the following statements correctly describes the behaviour of the differential equation near the singular point x_2?:
    A. All solutions remain bounded near x_2.
    B. At least one non-zero solution remains bounded near x_2 and at least one solution is unbounded near x_2.
    C. All non-zero solutions are unbounded near x_2.

    Answers:
    (i) x_1 = 2 and x_2 = 2
    (ii) C
    (iii) B
    ================================================== ==================================================
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