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Math Help - Slope Fields and horizontal segments

  1. #1
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    Slope Fields and horizontal segments

    I am not really sure how to start this problem:

    The slope field of the differential equation is dy/dx=(x^2y+y^2x)/3x+y will have horizontal segments when...

    How do I find the horizontal segments without a calculator. I think I need to integrate, but I'm not sure.
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  2. #2
    Super Member redsoxfan325's Avatar
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    Quote Originally Posted by Moderatelyconfused View Post
    I am not really sure how to start this problem:

    The slope field of the differential equation is dy/dx=(x^2y+y^2x)/3x+y will have horizontal segments when...

    How do I find the horizontal segments without a calculator. I think I need to integrate, but I'm not sure.
    Do you mean this:
    \frac{dy}{dx} = \frac{x^2 y+y^2 x}{3x}+y

    or this:
    \frac{dy}{dx} = \frac{x^{2y}+y^{2x}}{3x}+y

    ?
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  3. #3
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    I meant: dy/dx=(x^2y+y^2x)/(3x+y)

    I apologize, the y was actually part of the denominator.
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  4. #4
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    Quote Originally Posted by Moderatelyconfused View Post
    I am not really sure how to start this problem:

    The slope field of the differential equation is dy/dx=(x^2y+y^2x)/3x+y will have horizontal segments when...

    How do I find the horizontal segments without a calculator. I think I need to integrate, but I'm not sure.
    dy/dx = 0 when the numerator is equal to zero (but check that the denominator doesn't also equal zero when this happens).
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