x[t_, s_] := 
      (1/2) (E^(2 *t))* (s^2)
y[t_, s_] := s*(E^t)
u[t_, s_] := 0
ParametricPlot3D[{x[t, s], y[t, s], u[t, s]}, {s, -1, 
          1}, {t, -1, 
          1}];