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Slope Fields with Mathematica
Equations of the Form: dy/dx = g(y)
Autonomous Equations
General Observations
The common themes that you should have noticed throughout the set of
exercises are the following:
The slope fields of all of the differential equations in this class have
horizontal isoclines. This makes sense when you think about it.
The equation
itself basically is another way of saying:
slope = g(y)
Hence, the slope at any point only depends on y, and never on
x. If you move left or right to various points on a horizontal line
then only their x-value changes, not their y-value, which leads to no
change in the slope. Hence, horizontal lines are isoclines. - All of the differential equations in this class are solvable by
direct integration, (assuming that the integral is analytically possible.)
Let's now go back to the main exercise menu.
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