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Math Help - Need Help with second order DE with constant coefficients.

  1. #1
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    Need Help with second order DE with constant coefficients.

    Hello - i need little help with this:
    Find the particular solution:



    blue - the problem
    black - part of the solution
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  2. #2
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    Have you taken the derivative of y?

    You need to set y(0) = 2 and y'(0) = -2
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  3. #3
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    Use the conditions y(0) = 2, and y'(0) = -2

    y(0) = (c1) + (c2) = 2
    y'(0) = -3(c1) + (c2)/3 = -2

    Solve for c1 and c2

    And you have the particular solution for y
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  4. #4
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    This is a homogeneous DE, you don't need to find a particular solution.

    Just substitute your boundary conditions, noting that \displaystyle y' = -3c_1e^{-3x} + \frac{c_2}{3}e^{\frac{x}{3}}, to evaluate \displaystyle c_1 and \displaystyle c_2.
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  5. #5
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    So what's the problem? You've already done the hard part. Insert the conditions y(0)=2 and y'(0)=-2 into your solution (and the derivative of it) and you'll end up with a system of linear equations that is easy to solve.
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  6. #6
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    OK thanks i just wanted to be sure.. Thanks for the help
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