...

>Differential Equations>Integral Curves and Direction Fields in GeoGebra

Integral Curves and Direction Fields in GeoGebra

You can use GeoGebra to draw the 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 View in Menu.
2.: For each particular solution you want to draw, type

f(x) := <the particular solution>

into Algebra View. Press Enter.
3.: Do this as many times as necessary 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 View in Menu.
2.: Type SlopeField(<f(x, y)>) into Algebra View. Type the expression for $y^{'}$ as <f(x,y)>. Press Enter.

Screenshot of GeoGebra showing a direction field for a differential equation

How to Write and Solve a Differential Equation in GeoGebra