ClearAll["Global`*"];f1 = (3y/(x-1)); (*cviko, př. 1*)

rce1=f1/.{y -> y[x]};  Manipulate[PocPodm = {p1,p1};a1 = VectorPlot[{1,f1},{x,-3,3},{y,-3,3}, Axes->True, AxesStyle->Thick];
b1 = ParametricPlot[{1,u},{u,-3.2,3.2}, PlotStyle->{RGBColor[1,0,0], Thickness[0.01]}];s1=NDSolve[{y'[x] ==rce1, y[PocPodm[[1]]]== PocPodm[[2]]}, y, {x,-2.5,0}];
t1=Plot[Evaluate[y[x]/.s1],{x,-2.5,2.5},PlotRange->All, PlotStyle->{RGBColor[0,255,0]}]; d1=Graphics[ {PointSize[0.03],Point[PocPodm]}]; Show[a1,b1,t1,d1, ImageSize->Large], {p1,DeleteElements[Range[-2,2,1/2], {1}], SetterBar}]

rce2=f1/.{y -> y[x]};  Manipulate[PocPodm = i;a = VectorPlot[{1,f1},{x,-3,3},{y,-10,10}, Axes->True, AxesStyle->Thick];
b = ParametricPlot[{1,u},{u,-10,10}, PlotStyle->{RGBColor[1,0,0], Thickness[0.005]}];s=NDSolve[{y'[x] ==rce2, y[PocPodm[[1]]]== PocPodm[[2]]}, y, {x,-2.5,0}];
t=Plot[Evaluate[y[x]/.s],{x,-2.5,2.5},PlotRange->All, PlotStyle->{RGBColor[0,255,0]}]; d=Graphics[ {PointSize[0.03],Point[PocPodm]}]; Show[a,b,t,d, ImageSize->Large], {i,{{-1,-8},{2,8}, {1,8}},SetterBar}]

(*cviko, př. 2*)

f3 = (E^x/2y);rce3=f3/.{y -> y[x]};  Manipulate[PocPodm = p;a3 = VectorPlot[{1,f3},{x,-3,3},{y,-3,3}, Axes->True, AxesStyle->Thick];
b3 = ParametricPlot[{u,0},{u,-3.2,3.2}, PlotStyle->{RGBColor[1,0,0], Thickness[0.01]}];s3=NDSolve[{y'[x] ==rce3, y[PocPodm[[1]]]== PocPodm[[2]]}, y, {x,-2.5,3}];
t3=Plot[Evaluate[y[x]/.s3],{x,-2.5,3},PlotRange->All, PlotStyle->{RGBColor[0,255,0]}]; d3=Graphics[ {PointSize[0.03],Point[PocPodm]}]; Show[a3,b3,t3,d3, ImageSize->Medium], {p,{{0,2}, {0,-1}, {1,0},{1.9,0.1}}, SetterBar}]

ClearAll["Global`*"]; fce=(2x*y)/(x^2-1); (*fce z příkladu č.1 v prvním úkolu*)

(*rce=fce/.{y -> y[x]};  Manipulate[PocPodm = {p,p};a = VectorPlot[{1,fce},{x,-3,3},{y,-3,3}, Axes->True, AxesStyle->Thick];
b = ParametricPlot[{1,u},{u,-3.2,3.2}, PlotStyle->{RGBColor[1,0,0], Thickness[0.01}];c= ParametricPlot[{-1,u},{u,-3.2,3.2}, PlotStyle->{RGBColor[1,0,0], Thickness[0.01}];s=NDSolve[{y'[x] ==rce, y[PocPodm[[1]]]== PocPodm[[2]]}, y, {x,-3,3}];
t=Plot[Evaluate[y[x]/.s],{x,-3,3},PlotRange->All, PlotStyle->{RGBColor[0,255,0]}]; d=Graphics[ {PointSize[0.03],Point[PocPodm]}]; Show[a,b,c,t,d, ImageSize->Large], {p,-3,3}]*)