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Math Help - Orthogonal Trajectories .. Check my solution

  1. #1
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    Orthogonal Trajectories .. Check my solution #1

    Hello

    Problem:
    Find the orthogonal trajectories of the following family of curves:
    x^n+y^n=a^n ; n held fixes, n \neq 2

    Solution:
    Differentiate with respect to x:

    nx^{n-1}+ny^{n-1} \cdot \dfrac{dy}{dx}=0

    devide by n and re-arrange:

    \dfrac{dy}{dx} = - \dfrac{x^{n-1}}{y^{n-1}}

    the equation for orthogonal family:

    \dfrac{dy}{dx} = \dfrac{y^{n-1}}{x^{n-1}}

    which is separable:

    y^{1-n} dy = x^{1-n} dx

    Solving:

    y^{2-n} = x^{2-n} + c .. which is the equation of orthogonal trajectories ..

    any mistakes?
    Last edited by Liverpool; October 10th 2010 at 06:58 AM.
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  2. #2
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    Krizalid's Avatar
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    looks good to me.
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  3. #3
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    Thanks.
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  4. #4
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    you already do it by clicking on the "thanks button," there's no need you to post a "thanks" again, it's enough with clicking the button.
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  5. #5
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    thanks again .
    I'll do it.
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