# PP 10.2 - Direction Fields and Eulers Method These are...

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Direction Fields and Euler’s Method These are tools available for approximating solutions of certain differential equations when explicit solutions can not be found.

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Direction Fields field. direction a to s correspond ) , ( form the of equation al differenti A y x g dx dy = A direction field assigns to each point (x,y) in the plane the direction of a tiny line segment with slope g(x,y). We can represent the direction at (x,y) by a vector (that is a little arrow) whose coordinates are (1, g(x,y)).
y dx dy 3 = xy dx dy 3 = Here are some examples of vector fields.

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) sin( x dx dy = ) sin( xy dx dy =
By following the arrows in a direction field, particular solutions of the equation can be plotted, as shown. This is useful when needing to approximate a solution that can not be found directly.

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Direction fields are NOT easily constructed by hand. A calculator or a CAS is better for such a task. Here is the Maple command for plotting a
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PP 10.2 - Direction Fields and Eulers Method These are...

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