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Math Help - Help with this differential equation?

  1. #1
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    Feb 2010
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    Help with this differential equation?

    d^2x/dt^2 - dx/dt - 12x = 0, where x = 12 and dx/dt = 13 when t = 0

    Could I have a full explaination to this question?
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  2. #2
    Super Member Deadstar's Avatar
    Joined
    Oct 2007
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    Strong user name to slightly trollish question.

    I'll try to translate what I think is going on anyway...

    You're given...

    \frac{d^2x}{dt^2} - \frac{dx}{dt} - 12x = 0.

    You should be able to solve this to find some function of t.

    Then! You can use that other part of the question...

    That part is known as the initial conditions. You plug the t value into the formula you found and solve it based on the value it tells you it should be.

    So lets say, for example, [THIS IS NOT THE ANSWER.]

    You solved the above and found that...

    x(t) = 3t^2 + c

    You're given at the start of the question that x = 12 when t = 0.

    Hence plug t into x(t) and you get x(0) = 0 + c = 12, hence c = 12.

    You will have to do the same except you will also need to find the derivative and sub in t=0 to that.
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