I want to plot the solution of a differential equation in a widget which lets me select an initial point of space and let it evolve according to the equation using an slider.
My code looks like this:
f[x_,y_]:=x-y+(x*y-x^3-x*y^2)/Sqrt[x^2 + y^2] g[x_,y_]:=x+y-(x^2+x^2*y+y^3)/Sqrt[x^2 + y^2] Manipulate[ Module[{sol = NDSolve[{x'[t]==f[x[t],y[t]],y'[t] == g[x[t],y[t]], x[0] == p[[1]], y[0] == p[[2]]}, t,{y,0,T}, {x, 0, T}]}, ParametricPlot[Evaluate[{x[t], y[t]} /. sol], {t, 0, T}, PlotRange -> {{-4, 4}, {-3, 3}}]], {{p, {2, 1}}, Locator}, {{T, 10}, 0, 100}]
But while the slider is being shown, it does not behave correctly (the trajectory of each point is not being shown).
What is going on? How do I fix it?