Needs["VisualDSolve`"]

?VisualDSolve

\(TraditionalForm
    \`pic02 = 
      VisualDSolve[
        \(y'\)[t] == y[t] Sin[y[t] - t], {t, \(-5\), 5}, {y, \(-4\), 4}, 
        DirectionField -> True, PlotStyle -> {AbsoluteThickness[2], Red}, 
        FieldColor -> Blue, FieldMeshSize -> 20]\)

\(TraditionalForm
    \`Display["pic02.gif", pic02, "GIF", ImageSize -> {500, 309}]\)

\(TraditionalForm
    \`pic03 = 
      VisualDSolve[
        \(y'\)[t] == y[t]\ Sin[y[t] - t], {t, \(-5\), 5}, {y, \(-4\), 4}, 
        DirectionField -> True, PlotStyle -> {AbsoluteThickness[2], Red}, 
        FieldColor -> Blue, InitialValues -> Grid[2], 
        ShowInitialValues -> True, FieldMeshSize -> 20]\)

\(TraditionalForm
    \`Display["pic03.gif", pic03, "GIF", ImageSize -> {500, 309}]\)

\(TraditionalForm
    \`\(pic04 = 
      Plot[.2  y\ \((5 - y)\) \((y - 2)\), {y, \(-1\), 7}, 
        PlotStyle -> {AbsoluteThickness[2], Blue}, AxesLabel -> {y, y'}, 
        Epilog -> {AbsolutePointSize[7], Point[{0, 0}], Point[{2, 0}], 
            Point[{5, 0}]}]; \)\)

\(TraditionalForm
    \`Display["pic04.gif", pic04, "GIF", ImageSize -> {500, 309}]\)

\(TraditionalForm
    \`pic05 = 
      VisualDSolve[
        \(y'\)[t] == .2\ y[t] \((5 - y[t])\) \((y[t] - 2)\), {t, 0, 4}, {y, 
          0, 7}, DirectionField -> True, 
        PlotStyle -> {AbsoluteThickness[2], Red}, FieldColor -> Blue, 
        InitialValues
           -> {{0, 0}, {0, 5}, {0, 2}, {0, 1.7}, {0, 2.2}, {0, 7}, {2, 1.7}, {
              2, 5}, {2, 2.2}, {2, 7}}, FieldMeshSize -> 20, 
        AxesLabel -> {t, y}]\)

\(TraditionalForm
    \`Display["pic05.gif", pic05, "GIF", ImageSize -> {500, 309}]\)

\(TraditionalForm
    \`pic06 = 
      Do[VisualDSolve[
          \(y'\)[t] == .2\ y[t] \((5 - y[t])\) - h, {t, 0, 10}, {y, 0, 7}, 
          DirectionField -> True, PlotStyle -> {AbsoluteThickness[2], Red}, 
          FieldColor -> Blue, 
          InitialValues
             -> {{5, 5/2 + Sqrt[25/4 - 5  h]}, 

              					{5, 5/2 - Sqrt[25/4 - 5  h]}, 
              	{0, .9 \((5/2 - Sqrt[25/4 - 5  h])\)}, 

              						{0, \((5/2 - Sqrt[25/4 - 5  h])\) + .1}, {0, 4}, 

              						{5, \((5/2 - Sqrt[25/4 - 5  h])\) + .1}, {0, 7}, {
                5, 7}}, FieldMeshSize -> 20, AxesLabel -> {t, y}, 
          MaxSteps -> 1000, 
          PlotLabel -> StringForm["h=`1`", PaddedForm[N[h], {4, 3}]], 

          			Epilog
             -> {AbsolutePointSize[7], Point[{0, 5/2 + Sqrt[25/4 - 5  h]}], 

              					Point[	{0, 5/2 - Sqrt[25/4 - 5  h]}]}], 

        		{h, 0, 3/2, 1/40}]\)

[

\(TraditionalForm\`counter = 1; 

    Do[{Print[
          PaddedForm[counter, 2, NumberPadding -> {"0", ""}]]; 

        	picture = 
          VisualDSolve[
            \(y'\)[t] == .2\ y[t] \((5 - y[t])\) - h, {t, 0, 10}, {y, 0, 7}, 
            DirectionField -> True, PlotStyle -> {AbsoluteThickness[2], Red}, 
            FieldColor -> Blue, 
            InitialValues
               -> {{5, 5/2 + Sqrt[25/4 - 5  h]}, 

                					{5, 5/2 - Sqrt[25/4 - 5  h]}, 
                	{0, .9 \((5/2 - Sqrt[25/4 - 5  h])\)}, 

                						{0, \((5/2 - Sqrt[25/4 - 5  h])\) + .1}, {0, 4}, 
                
						{5, \((5/2 - Sqrt[25/4 - 5  h])\) + .1}, {0, 
                  7}, {5, 7}}, FieldMeshSize -> 20, AxesLabel -> {t, y}, 
            MaxSteps -> 1000, 
            PlotLabel -> StringForm["h=`1`", PaddedForm[N[h], {4, 3}]], 

            			Epilog
               -> {AbsolutePointSize[7], Point[{0, 5/2 + Sqrt[25/4 - 5  h]}], 
                
					Point[	{0, 5/2 - Sqrt[25/4 - 5  h]}]}]; 
		
        Display[
			
          StringJoin[
				
            ToString[
					
              PaddedForm[
						counter, \ 2, 
                NumberPadding -> {"0", ""}]], ".gif"], 
		
          picture, "GIF", ImageSize -> {500, 309}], \(counter++\)}, 

      		{h, 0, 3/2, 1/40}]\)