First-Order Differential Equations - The Geometry of First-Order Differential Equations

5 important questions on First-Order Differential Equations - The Geometry of First-Order Differential Equations

What is a slope field?

A sketch of segments of differential equation , where each segment has the slope .

Which procedures are there to create a slope field?

1. Isoclines
2. Equilibrium solution
3. Concavity change

What is the equilibrium solution?

The equilibrium solution is the solution to the differential equation where y(x) = y0 with y0 a constant. In a slope field is the equilibrium solution a line parallel to the x-axis.
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When are isoclines concave up?

When ,all solution curves are concave up.

When are the isoclines concave down?

All isoclines are concave down when .

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