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Math Help - Slope Field for Differential Equation

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    Slope Field for Differential Equation

    The slope field for the differential equation dy/dx=(3y)/(xy+5x) will have vertical segments when

    A) x=0, only
    B) y=0, only
    C) y=-5, only
    D) y=5, only
    E) x=0 or y=-5

    Im not sure what this question is asking for, we have never used the term slope field in class. I do know that something with a vertical slope has a derivative of undefined though. Please help
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    I think I answered my question. The slope field has vertical segments whenever the derivative is undefined. So I did trial in error with all my answer options and found that whenever x=0 or y=-5, the denominator of dy/dx=0 thus making it undefined, thus giving the slope field vertical segments.
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  3. #3
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    Quote Originally Posted by rawkstar View Post
    I think I answered my question. The slope field has vertical segments whenever the derivative is undefined. So I did trial in error with all my answer options and found that whenever x=0 or y=-5, the denominator of dy/dx=0 thus making it undefined, thus giving the slope field vertical segments.
    trial and error? what if the answer choices were not available?

    xy+5x = 0

    x(y+5) = 0

    x = 0 , y = -5
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