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Intros
Lessons
  1. What are Slope Fields?
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Examples
Lessons
  1. Understanding Slope Fields
    Find the directional field for the following equations:
    1. dydx=xyx \frac{dy}{dx}=xy-x
    2. dydx=x2(y+1) \frac{dy}{dx}=\frac{x^2}{(y+1)}
  2. Determining the Equation from a Slope Field
    Which equation best corresponds to the following slope field?
    Slope fields and corresponding differential equations

    i.
    dydx=y2\frac{dy}{dx}=y-2
    ii.
    dydx=xy2\frac{dy}{dx}=xy-2
    iii.
    dydx=x+1\frac{dy}{dx}=x+1
    iv.
    dydx=x+1\frac{dy}{dx}=-x+1
    1. Which equation best corresponds to the following slope field?
      determine the best corresponds differential equations of slope fields

      i.
      dydx=xy2\frac{dy}{dx}=xy-2
      ii.
      dydx=yx\frac{dy}{dx}=-\frac{y}{x}
      iii.
      dydx=2x+y\frac{dy}{dx}=2x+y
      iv.
      dydx=xy3\frac{dy}{dx}=xy-3
      1. Given the differential equation and its resulting slope field:
        dydx=y2(y3)\frac{dy}{dx}=\frac{y}{2}(y-3)
        Slope fields and differential equations

        Draw a solution to the following differential equation using the following initial value conditions:
        1. y(2)=1y(-2)=1
        2. y(0)=4 y(0)=4
        3. y(1)=3 y(1)=3
      Topic Notes
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      Slope fields, also called directional fields or vector fields, are graphical representations of first-order differential equations.

      Slope Fields consist of a bunch of lines indicating the slope of y with respect to x, or dydx\frac{dy}{dx}