E 1: Run exponential function and try the points and the trace option. After back try different step widths (speed). With the exponential you will see no difference within the given range of the slider.
E 2: Go back, and chose a new initial condition. Start creates the solution, which is different from the first one. Try the points and trace options.
E 3: Create a set of solutions with identical x0 and different y0. Explain what you see.
E 4: Create a set of solutions with identical y0 and different x0. Why do you see curves that are shifted parallel?
E 5: Create sets of solutions including negative initial values y0. Discuss the result as consequence of the differential equation.
E 6: Choose exponential damping. Compare solutions for positive and negative initial values to those of the exponential.
E 7: Choose any of the oscillating functions and try to guess the trace before calculation by studying the differential equation.
E 8: Edit the exponential by adding factors g(x), especially periodic ones. Try to understand what you observe.
E 9: Run the exponential once. Choose back. Edit the formula by setting e^x instead of y. In a second run you will see the same result: The algorithm now performs ordinary Integration (numerical calculation of the antiderivative = indefinite integral). This works for the exponential, because y is not explicit in dy/dx = e^x.
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E 10: Choose any other function not containing y, e.g. sin(x). For this you get -cos(x) as indefinite integral,with the initial value as integration constant. Compare the phase space diagram of Sine with that of the function type Periodical.
E11: Choose constant velocity and create a curve set for different factors y, including zero. This again is a simple integration. Edit the differential equation in such a way that an initial starting location (x0) is considered.
E12: Choose constant acceleration and create a curve set for different factors of y, including zero. This again is a simple integration. Edit the differential equation in such a way that an initial velocity is considered.
E 13: Extend the differential equation by more complicated functions of y and let yourself be surprised by what happens. Try to define and understand interrelated families of differential equations. Are there more classes than convergent, divergent, periodic?
E14: After back change the step width for different functions and observe the result. Which characteristics define the maximum width below which no deviations are observed?