Dynamically Adjust the Parameters of a Differential Equation
Use a phase plane plot with Manipulate to vary the initial conditions of a differential equation solved with NDSolve.
Manipulate[
Module[{sol = NDSolve[{y''[x] + Sin[y[x]] == 0, y[0] == p[[1]], y'[0] == p[[2]]}, y, {x, 0, T}]},
ParametricPlot[Evaluate[{y[x], y'[x]} /. sol], {x, 0, T}, PlotRange -> {{-4, 4}, {-3, 3}}]],
{{p, {2, 1}}, Locator}, {{T, 10}, 0, 100}]