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Differential Equations

Using the GeoGebra command solveODE you can illustrate numerical solutions to first and second order ordinary differential equations.

First order differential equations

When using the command solveODE, \(y\) must be a function of \(x\). Let

\[\frac{dy}{dx} = f(x,y)\]

then you can used the commands:

solveODE(f)
solveODE(f, <Point on f>)
solveODE(f, <Start x>, <Start y>, <End x>, <Step>)

and:

SlopeField(f)
SlopeField(f, <Number n>)
SlopeField(f, <Number n>, <Length multiplier a>)

If the solution curve has vertical points and if the equation can be written as

\[\frac{dy}{dx} = \frac{f(x,y)}{g(x,y)}\]

it is better to use the command

solveODE(f, g, x(A), y(A), <End t>, <Step> )

where A is a point on the curve. This command is used in the worksheet above.

The command

SolveODE[<b(x)>,<c(x)>,<f(x)>,<Start x>,<Start y>,<Start y'>,<End x>,<Step> ]

solves the equation

\[y''+b(x)y'+c(x)y=f(x)\]

First order ODE

Make the function

\[f(x, y) = y\sin(x) + \frac{y}{x}.\]

Link an input box to the function so you easily can redefine it.

Make a point \(A\).

Make a slope field and solve the equation numerically.

by Malin Christersson under a Creative Commons Attribution-Noncommercial-Share Alike 2.5 Sweden License

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