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Math Help - help with a differential equation

  1. #1
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    help with a differential equation

    Can anyone solve the Abel differential equation

    x y \frac{dy}{dx} = x + y

    It looks so easy
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  2. #2
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    Hi!


    Quote Originally Posted by danny arrigo View Post
    Can anyone solve the Abel differential equation

    x y \frac{dy}{dx} = x + y

    It looks so easy
    Edit: Aaaargh, mr fantastic is right,
    Edit: the following is the wrong:

     x*y \frac{dy}{dx} = x+y

     x*y - y \frac{dy}{dx} = x

     y (x-1) \frac{dy}{dx} = x

     y \frac{dy}{dx} = \frac{x}{x-1}

     \int y \frac{dy} = \int \frac{x}{x-1} dx

     0.5y^2 = ln(x - 1) + x + c

    ....

    Can you solve it now?

    Edit: I made a big mistake... Sorry

    Merry christmas,
    Rapha
    Last edited by Rapha; December 25th 2008 at 08:14 PM.
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  3. #3
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    Quote Originally Posted by Rapha View Post
    Hi!




     x*y \frac{dy}{dx} = x+y

    Mr F asks: How do the following lines follow from the above .....?

     x*y - y \frac{dy}{dx} = x

     y (x-1) \frac{dy}{dx} = x

     y \frac{dy}{dx} = \frac{x}{x-1}

     \int y \frac{dy} = \int \frac{x}{x-1} dx

     0.5y^2 = ln(x - 1) + x + c

    ....

    Can you solve it now?

    Merry christmas,
    Rapha
    Quote Originally Posted by danny arrigo View Post
    Can anyone solve the Abel differential equation



    x y \frac{dy}{dx} = x + y



    It looks so easy
    I have no time now but I think the first thing to do is make the substitution y = 1/v.
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  4. #4
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    Quote Originally Posted by mr fantastic View Post
    I have no time now but I think the first thing to do is make the substitution y = 1/v.
    This substitution turns my Abel equation of the second kind to one of the first kind which I still don't know how to solve!
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  5. #5
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    Quote Originally Posted by danny arrigo View Post
    This substitution turns my Abel equation of the second kind to one of the first kind which I still don't know how to solve!
    In the meantime, you might have a read of http://www.cecm.sfu.ca/CAG/papers/edgardoEJAM04.pdf
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  6. #6
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    Quote Originally Posted by mr fantastic View Post
    In the meantime, you might have a read of http://www.cecm.sfu.ca/CAG/papers/edgardoEJAM04.pdf
    Yes, I know of Cheb-Terrab paper.
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  7. #7
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    Generally speaking, equations that have attracted enough interest to be given their own names are very difficult!
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