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Math Help - y remains finite for large values of x

  1. #1
    Super Member craig's Avatar
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    y remains finite for large values of x

    Hi again, just a quick question about the wording of a question.

    I have the General Solution to a differential equation:

    y = Ae^{3x} + Be^{-2x} + \frac{1}{6} (\cos{3x} - \sin{3x})

    We are given the fact that when y=1, x=0.

    From this fact I've got the equation A+B = \frac{5}{6}

    The only other information we are given is that y remains finite for large values of x.

    Here's how I interpreted this, can someone please just verify that this is right.

    When x is large, then Be^{-2x} tends towards 0, we can then discount this from out equation.

    When x gets larger, Ae^{3x} eventually goes towards infinity, but the question states that y remains finite, therefore A = 0.

    The final solution I have got then is:

    y = \frac{5}{6}e^{-2x} + \frac{1}{6} (\cos{3x} - \sin{3x}).

    Is this correct?

    Thanks
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  2. #2
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    skeeter's Avatar
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    Quote Originally Posted by craig View Post
    Hi again, just a quick question about the wording of a question.

    I have the General Solution to a differential equation:

    y = Ae^{3x} + Be^{-2x} + \frac{1}{6} (\cos{3x} - \sin{3x})

    We are given the fact that when y=1, x=0.

    From this fact I've got the equation A+B = \frac{5}{6}

    The only other information we are given is that y remains finite for large values of x.

    Here's how I interpreted this, can someone please just verify that this is right.

    When x is large, then Be^{-2x} tends towards 0, we can then discount this from out equation.

    When x gets larger, Ae^{3x} eventually goes towards infinity, but the question states that y remains finite, therefore A = 0.

    The final solution I have got then is:

    y = \frac{5}{6}e^{-2x} + \frac{1}{6} (\cos{3x} - \sin{3x}).

    Is this correct?

    Thanks
    looks like you covered all the bases to me.
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  3. #3
    Super Member craig's Avatar
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    Thanks for the reply.

    I hadn't heard of this notation before, was just wondering if I'd done it right.
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  4. #4
    MHF Contributor matheagle's Avatar
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    yes, y remains finite for large values of x implies that A=0
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