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Math Help - Is an exponential solution the correct thing to try here?

  1. #1
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    Is an exponential solution the correct thing to try here?

    Hi all,

    I have an ODE of the form X" + aX' + (bc)^2 X = 0.

    Is the correct way of solving this to try an exponential solution of the form Ae^rx?
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  2. #2
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    Assuming a,b, and c are constant it could be of this form, have you solved your charateristic equation yet? What did you get?
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  3. #3
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    Yes, a,b and c are constants, sorry I forgot to put that in.

    It becomes a quadratic equation:

    r^2 + ar + (bc)^2 = 0.

    The quadratic formula gives

    r = [-a + sqrt(a^2 - 4(bc)^2)]/2 and
    r = [-a - sqrt(a^2 - 4(bc)^2)]/2.

    I note that there will be two independent solutions when the discrimant is positive, that is, when

    a^2 - 4(bc)^2 > 0, or

    a^2 > 4(bc)^2, or

    |a| > |2bc|
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