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Math Help - Find General Solution

  1. #1
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    Find General Solution

    Find the general solution of y'' - iy' + 6y = 0.

    I know how to solve these, but the 'i' is throwing me off on this one...

    Can someone show this one? Thanks a lot...
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  2. #2
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    Have you found and solved the characteristic equation?
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  3. #3
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    The first thing i did was write: r^2 - ir + 6 = 0
    Then factored it to be (r+2i)(r-3i) = 0
    So,
    r = -2i and 3i

    What from here? THanks.
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  4. #4
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    Sounds like a good start. So you have complex solutions to your charateristic equation.

    What general form should you use?

    This example is really good to follow. Homogeneous linear equations with constant coefficients
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  5. #5
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    The problem that I'm having is this:

    a = 0, but b = -2 AND b = 3

    So, would my general solution look something like this? What am I missing?
    y(x) = e^0 (c1cos(-2) + c2sin(3)
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  6. #6
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    Quote Originally Posted by jzellt View Post
    The problem that I'm having is this:

    a = 0, but b = -2 AND b = 3

    So, would my general solution look something like this? What am I missing?
    y(x) = e^0 (c1cos(-2) + c2sin(3)
    you're close

    as e^0=1 then y(x) = c_1\cos(\beta x) + c_2\sin(\beta x)

    But now we have an additinal problem as the solutions aren't complex conjugates.
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  7. #7
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    Exactly... Thats my problem. What do I do from here?
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  8. #8
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    Quote Originally Posted by jzellt View Post
    Exactly... Thats my problem. What do I do from here?
    Since the DE is complex, why can't you just give y = A e^{3ix} + B e^{-2ix} as the solution ....?
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  9. #9
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    Yeah, not sure why I didn't realize that a first, but the important thing is that eventually I figured it out. Thanks
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