dx/dt = f(x, y, t) dy/dt = g(x, y, t)in terms of the initial condition x=x0, y=y0 at t=t0:
x = A(x0, y0, t0, t) y = B(x0, y0, t0, t)then you can plug it in the applet and see if blue curves (numerical solutions) coincide with red curves (obtained from your formula). You can also use this method to verify whether your formula holds for some particular initial conditions. In the example below, we compare the solution to the equation d^2x/dt^2 = t + x - x^2 to its Taylor series solution. First, this equation is re-written as a system of two equations:
dx/dt = y dy/dt = t + x - x^2and the resulting system is fed into the applet.
View Instructions on using the Applet
Marek Rychlik (rychlik@u.arizona.edu)
Author's Home Page: http://alamos.math.arizona.edu