(* Solution curves of x'[t] == Sin[t*x[t]]. 
   Background is shaded to show slope of curves; 
   black lines correspond to zero slope (nullclines).  
   This example is on p. 27 of "VisualDSolve" by Dan 
   Schwalbe and Stan Wagon  *)

Needs["VisualDSolve`"];

VisualDSolve[x'[t] == Sin[t*x[t]], {t, -1, 6}, {x, -1, 7},
    InitialValues -> Table[{0, x}, {x, -0.75, 6, 0.5}],
    IsoclineShading -> True, Contours -> 10, IsoclinePlotPoints -> 100,
    Isoclines -> True, IsoclineStyle -> AbsoluteThickness[1.5], 
    Rainbow -> True, PlotStyle -> AbsoluteThickness[2], 
    AspectRatio -> .9];