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Math Help - Differential Slope Field Help

  1. #1
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    Differential Slope Field Help

    Consider the differential equation dy/dx=xy^2
    A) on the axes provided sketch a slope field for the given differential equation at the nine points indicated [(-1,-1) (-1,0) (-1,1) (0,-1) (0,0) (0,1) (1,-1) (1,0) (1,1)]
    B)find the general solution of the given differential equation in terms of aconstant C
    C)Find the particular solution of the differential condition that satisfies the initial condition y(0)=1
    D) For what values of the constant C will the solutions of the differential equation have on or more vertical asymptotes? Justify your answers

    I have no idea where or how to begin Please Help!
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  2. #2
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    anybody? i figured out part A
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    Quote Originally Posted by rawkstar View Post
    Consider the differential equation dy/dx=xy^2
    A) on the axes provided sketch a slope field for the given differential equation at the nine points indicated [(-1,-1) (-1,0) (-1,1) (0,-1) (0,0) (0,1) (1,-1) (1,0) (1,1)]
    For the first point (-1, -1) find dy/dx

    \frac{dy}{dx}=(-1)(-1)^2=-1

    Through the point (-1, -1) sketch a short segment with slope -1

    Do the same for each of the other points
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  4. #4
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    already did, thanks though
    I'm just still confused with B C & D although I did get a little hint
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    Quote Originally Posted by rawkstar View Post
    Consider the differential equation dy/dx=xy^2
    B)find the general solution of the given differential equation in terms of aconstant C
    I have no idea where or how to begin Please Help!
    \frac{dy}{dx}=xy^2

    \frac{dy}{y^2}=x\,dx

    -\frac{1}{y}=\frac{1}{2}x^2+C

    y=-\frac{2}{x^2+2C}
    Last edited by ione; March 28th 2010 at 06:28 PM.
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  6. #6
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    Thank you, I'm pretty sure I can figure out C from that.
    I'm not sure how to do D though, I know you get a vertical asymptote when the denominator equals 0 or is undefined. However I'm not sure to do that when you don't know x and theyre asking for values of C
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  7. #7
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    Quote Originally Posted by rawkstar View Post
    Consider the differential equation dy/dx=xy^2
    A) on the axes provided sketch a slope field for the given differential equation at the nine points indicated [(-1,-1) (-1,0) (-1,1) (0,-1) (0,0) (0,1) (1,-1) (1,0) (1,1)]
    B)find the general solution of the given differential equation in terms of aconstant C
    \frac{dy}{dx}= xy^2 is equivalent to \frac{dy}{y^2}= \frac{x dx}. Integrate both sides.

    C)Find the particular solution of the differential condition that satisfies the initial condition y(0)=1
    Your answer to B will, of course, include a "constant of integration. Set x= 0, y= 1 and determine what that constant is.

    D) For what values of the constant C will the solutions of the differential equation have on or more vertical asymptotes? Justify your answers
    Presumably your solution to B will be of the form y= a rational function with both x and C in the denominator. For what values of C is there some value of x that makes the denominator 0?

    I have no idea where or how to begin Please Help!
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