1.2 Diretion Fields

y’=f(x,y)

y’ = y + x

VectorPlot[{1,y+x},{x,-2,2},{y,-2,2},VectorScale->{Tiny, Automatic,None},Axes->True]

y’ = xy

VectorPlot[{1,x y},{x,-3,3},{y,-3,3},VectorScale->{Tiny, Automatic,None},Axes->True]

VectorPlot[{1,0.1 (1-x^2)-x/y},{x,-3,3},{y,-3,3},VectorScale->{Tiny, Automatic,None},Axes->True]

VectorPlot[{1,0.1(1-(x^2))-(x/y)},{x,-4,4},{y,-4,4},VectorScale->{Tiny,Automatic,None},Axes->True]

VectorPlot[{1,Exp[x]-y},{x,-3,3},{y,-3,3},VectorScale->{Tiny, Automatic,None},Axes->True]

VectorPlot[{1,1+y^2},{x,-Pi,Pi},{y,-2,2},VectorScale->{Tiny, Automatic,None},Axes->True]

Show[%21,Plot[Tan[x],{x,-Pi,Pi},PlotRange->{{-Pi,Pi},{-2,2}},PlotStyle->{Red, Thickness[0.01]}],
ListPlot[{{0.25 Pi,1}},PlotMarkers->{Automatic,Large}]]