This simulation displays the graphs for a first-order and second-order differential equation, determined by the function selected in the combo box.
The graph on the left shows the original curve y = f(x). The graph on the right shows the graph of y' against y (in blue) and the graph of y'' against y (in red).
The graphs can be viewed either as a set of points or as a continuous trace, by selecting the respective option on the top of the simulation. Press the reset button to reset the simulation, and the play button to play it (this may be intuitive for most users, but I hear that this instruction is occasionally useful.)

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