## DiffEq Applet

DiffEq is used in a variety of ways. It can be used to show the general idea of a differential equation, showing a specific solution with a draggable initial condition. It can also show a slope field, or an animated Euler's method. Optional sliders can be shown for parameters like k and L, useable in the differential equation for exponential growth/decay and logistic growth.

The applet tag that creates the applet is as follows:

<applet code="net.sourceforge.webcompmath.calculus.DiffEq" codebase="../../assets"

archive="webcompmath.jar,calculus.jar" height="400" width="640">

<param name="UseLoadButton" value="no" />

<param name="Example1" value="1. Deriv. is a Line;2x;0;3;-5,5,-5,5" />

<param name="Example2" value="2. Deriv. is cos;cos(x);0;1;-6.28,6.28,-5,5" />

<param name="ShowOriginSolution" value="yes" />

</applet>

This applet takes the following parameters:

Param NameTypeDefaultDescriptionExample1, ...String N/A Each example is a list of strings separated by semicolons. The strings, in order, are:

1. The name of the example, displayed in the example menu.

2. The expression for the differential equation dy/dx. Both x and y can be used in the expression.

3. The initial x value for the initial condition.

4. The initial y value for the initial condition.

5. The xmin, xmax, ymin and ymax values for the graph region, separated by commas.

6. The value for k.

7. The value for L.

8. The value for deltaTShowOriginSolutionyes/no no If "yes", graphs a solution through the origin (this is separate from the solution through the draggable initial condition). ShowSlopeFieldyes/no no If "yes", shows a slope field for the differential equation. ShowKyes/no no If "yes", shows the k parameter input box and slider. k can then be used in the differential equation. ShowLyes/no no If "yes", shows the L parameter input box and slider. L can then be used in the differential equation. ShowEuleryes/no no If "yes", shows animation control parameters and a deltaT input box and slider for use with Euler's method.