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Math Help - dy/dx = ky

  1. #1
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    dy/dx = ky

    another problem just want to check im doing it right?
    ....solve differential equation leaving unknown letter K in constant

    \frac{dy}{dx}=ky

    dy = ky dx

    y = \int ky + dx

    =k\frac{y^2}{2} dx

    \frac{1}{2}Ky^2 +C
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by decoy808 View Post
    another problem just want to check im doing it right?
    ....solve differential equation leaving unknown letter K in constant

    \frac{dy}{dx}=ky

    dy = ky dx

    y = \int ky + dx

    =k\frac{y^2}{2} dx

    \frac{1}{2}Ky^2 +C
    Actually
    \displaystyle \frac{dy}{y} = k~dx

    Take it from here...

    -Dan
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  3. #3
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    is the answer

    y = Kx + C

    ?
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  4. #4
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    e^(i*pi)'s Avatar
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    No, you need to integrate the LHS as well.

    \ln |y| = kx + C
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  5. #5
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    thanks
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  6. #6
    Super Member TheChaz's Avatar
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    As a side note, if we drop the "k", we are left with
    dy/dx = y
    In other words, there is a function whose derivative is the function itself.
    Have you come across such a function in calculus?
    (I hope so!)

    Such a function is often used to model growth and decay...
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