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Thread: Vector field problem with unknown constans

  1. #1
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    Post Vector field problem with unknown constans

    If F is the vector field outside of the origin defined by

    F(x,y)=[(ax+by)/(x^2+y^2),(cx+dy)/(x^2+y^2)]

    Where

    D={(x,y) : y>0}

    Question: for which values of a,b,c & d is F conservative on the range D
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  2. #2
    MHF Contributor

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    Re: Vector field problem with unknown constans

    A vector field, v= f(x,y)i+ g(x,y)j is "conservative" if and only if \frac{\partial f}{\partial x}= \frac{\partial g}{\partial y} and \frac{\partial f}{\partial y}= -\frac{\partial g}{\partial x}.
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