Slope fields

Lessons

• Introduction
  What are Slope Fields?

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• 1.
  Understanding Slope Fields
  Find the directional field for the following equations:
  a)

  $\frac{dy}{dx}=xy-x$
  
  
  b)

  $\frac{dy}{dx}=\frac{x^2}{(y+1)}$
  
  

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• 2.
  Determining the Equation from a Slope Field
  Which equation best corresponds to the following slope field?
  
  
  i.

  $\frac{dy}{dx}=y-2$
  ii.

  $\frac{dy}{dx}=xy-2$
  iii.

  $\frac{dy}{dx}=x+1$
  iv.

  $\frac{dy}{dx}=-x+1$
  

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• 3.
  Which equation best corresponds to the following slope field?
  
  
  i.

  $\frac{dy}{dx}=xy-2$
  ii.

  $\frac{dy}{dx}=-\frac{y}{x}$
  iii.

  $\frac{dy}{dx}=2x+y$
  iv.

  $\frac{dy}{dx}=xy-3$
  

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• 4.
  Given the differential equation and its resulting slope field:
  $\frac{dy}{dx}=\frac{y}{2}(y-3)$
  
  
  Draw a solution to the following differential equation using the following initial value conditions:
  a)

  $y(-2)=1$
  
  
  b)

  $y(0)=4$
  
  
  c)

  $y(1)=3$
  
  

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