x[θ_, t_] := 
      Cos[θ]*(E^t)
y[θ_, t_] := 
      Sin[θ]*(E^t)
u[θ_, 
        t_] := (E^(4*t))

    
t1 = {x[θ, 0], y[θ, 0], 
          u[θ, 0], {RGBColor[1, 0, 0], 
            Thickness[0.01]}};
t2 = {x[θ, 0.2], y[θ, 0.2], 
          u[θ, 0.2], {RGBColor[0, 1, 0], 
            Thickness[0.01]}};
t3 = {x[θ, 0.4], y[θ, 0.4], 
          u[θ, 0.4], {RGBColor[0, 0, 1], 
            Thickness[0.01]}};
tha1 = {x[0, t], y[0, t], 
          u[0, t], {RGBColor[1, 0, 0], 
            Thickness[0.01]}};
tha2 = {x[2*Pi/3, t], y[2*Pi/3, t], 
          u[2*Pi/3, t], {RGBColor[0, 1, 0], 
            Thickness[0.01]}};
tha3 = {x[4*Pi/3, t], y[4*Pi/3, t], 
          u[4*Pi/3, t], {RGBColor[0, 0, 1], 
            Thickness[0.01]}};

    
pt1 = 
        ParametricPlot3D[t1, {θ, 0, 2*Pi}, 
          DisplayFunction -> Identity];
pt2 = 
        ParametricPlot3D[t2, {θ, 0, 2*Pi}, 
          DisplayFunction -> Identity];
pt3 = 
        ParametricPlot3D[t3, {θ, 0, 2*Pi}, 
          DisplayFunction -> Identity];

    
ptha1 = 
        ParametricPlot3D[tha1, {t, 0, 0.6}, 
          DisplayFunction -> Identity];
ptha2 = 
        ParametricPlot3D[tha2, {t, 0, 0.6}, 
          DisplayFunction -> Identity];
ptha3 = 
        ParametricPlot3D[tha3, {t, 0, 0.6}, 
          DisplayFunction -> Identity];

    
wt1 = 
        Show[Graphics3D[{Text["t=0", {2, 1, 0}, {1, 1}]}], 
          DisplayFunction -> Identity];
wt2 = 
        Show[Graphics3D[{Text["t=0.2", {4, -0.8, 4}, {1, 1}]}], 
          DisplayFunction -> Identity];
wt3 = 
        Show[Graphics3D[{Text["t=0.4", {3.8, 0.5, 6}, {1, 1}]}], 
          DisplayFunction -> 
            Identity];

\(\(wtha1 = 
        Show[Graphics3D[{Text[\*""θ=\!\(0\^0\)"", {2.5, 2, 
                  9}, {1, 1}]}], 
          DisplayFunction -> Identity];\)\)
\(\(wtha2 = 
        Show[Graphics3D[{Text[\*""θ=\!\(120\^0\)"", {\(-0.5\), 
                  3.5, 9}, {1, 1}]}], 
          DisplayFunction -> Identity];\)\)
\(\(wtha3 = 
        Show[Graphics3D[{Text[\*""θ=(240^0)"", {\(-1.5\), \(-0.5\), 9}, {1, 1}]}], 
          DisplayFunction -> 
            Identity];\)
\)
w = 
      Show[wt1, wt2, wt3, wtha1, wtha2, wtha3, 
        DisplayFunction -> Identity, 
        PlotRange -> {{-5, 5}, {-5, 5}, {-1, 
              9}}]
pTotal = 
      Show[pt1, pt2, pt3, ptha1, ptha2, ptha3, 
        DisplayFunction -> Identity, 
        PlotRange -> {{-5, 5}, {-5, 5}, {-1, 
              9}}]
pExact = 
      Plot3D[((((x^2) + (y^2)))^2), {x, -5, 5}, {y, -5, 5}, 
        DisplayFunction -> Identity, 
        PlotRange -> {{-5, 5}, {-5, 5}, {-1, 
              9}}]



Show[pTotal, w, ImageSize -> {400, 300}, 
      DisplayFunction -> $DisplayFunction]
Show[pTotal, pExact, w, ImageSize -> {400, 300}, 
      DisplayFunction -> $DisplayFunction]