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Integral Curves and Direction Fields in GeoGebra

You can use GeoGebra to draw integral curves and direction fields of a differential equation.

To draw integral curves in GeoGebra, you need to find a particular solution of the differential equation for each curve you want to draw.

GeoGebra Instruction 1

Integral Curves

1.
Open Algebra View and Graphics View under GeoGebra icon View in GeoGebra icon Menu.
2.
For each particular solution you want to draw, type

f(x) := <the particular solution>

in Algebra View. Press Enter.

3.
Do this many times with different particular solutions if you are going to make a family of curves.

Screenshot of GeoGebra showing five integral curves for a differential equation

To draw direction fields, you have to solve the differential equation with respect to y first. That is, you have to write the differential equation so that y is isolated on the left-hand side of the equal sign. You do this because you need an expression for y.

GeoGebra Instruction 2

Direction Fields

1.
Open Algebra View and Graphics View under GeoGebra icon View in GeoGebra icon Menu.
2.
Type SlopeField(<f(x, y)>) in Algebra View. Type the expression for y as <f(x,y)>. Press Enter.

Screenshot of GeoGebra showing a direction field for a differential equation

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How to Write and Solve a Differential Equation in GeoGebra