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Math Help - Confusing Differential Equation

  1. #1
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    Confusing Differential Equation

    I'm trying to solve y'=-sqrt(|xy|).

    Not too sure on how to handle the absolute value signs.

    I've tried solving for +/-x and +/-y, but i couldn't find the constants because it involved negative square roots.

    Any ideas?

    Thanks
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  2. #2
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    Quote Originally Posted by benw View Post
    I'm trying to solve y'=-sqrt(|xy|).

    Not too sure on how to handle the absolute value signs.

    I've tried solving for +/-x and +/-y, but i couldn't find the constants because it involved negative square roots.

    Any ideas?

    Thanks
    Split it up into two equations, and solve them separately.

     \frac{dy}{dx} = - \sqrt{xy}

     \frac{dy}{dx} = - \sqrt{-xy}
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  3. #3
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    I tried doing that. For example y'=-sqrt(-xy)

    dx/sqrt(-x)=-sqrt(y)dy

    2x/sqrt(-x)+c=2.sqrt(y).y/3

    now say it is given that x(0)=1, c=sqrt(-1)/2(-1). I wouldn't be able to work out the constant here?

    Or does it simply mean that i do not need to solve for

    dx/sqrt(-x)=-sqrt(y)dy

    and only need to solve for

    dx/sqrt(x)=-sqrt(-y)dy?

    Thanks
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