"Punto silla, Dinámica y diagrama de fases cuando hay dos raíces reales de signos contrarios";

"Matriz, valores y vectores propios";
A={{3,-2},{2,-2}};
MatrixForm[A]
ValProp=Eigenvalues[A];
{ValProp[[1]],ValProp[[2]]}
VectProp=Eigenvectors[A];
{MatrixForm[VectProp[[1]]],MatrixForm[VectProp[[2]]]}

"Isoclinas, campo de vectores y trayectorias";
Isox=Solve[0=={3,-2}.{x,y},y];
Isoxx[x_]=Isox[[1,1,2]];
Isoy=Solve[0=={2,-2}.{x,y},y];
Isoyy[x_]=Isoy[[1,1,2]];
isoclinas=Plot[{Isoxx[x],Isoyy[x]},{x,-4,4},PlotRange->{-4,4},PlotStyle->Thick]
vectores=VectorPlot[{{3,-2}.{x,y},{2,-2}.{x,y}},{x,-4,4},{y,-4,4},VectorPoints->20];
sol11=DSolve[{x'[t]==3*x[t]-2*y[t],y'[t]==2*x[t]-2*y[t],x[0]==2,y[0]==4.0001},{x[t],y[t]},t];
sol22=DSolve[{x'[t]==3*x[t]-2*y[t],y'[t]==2*x[t]-2*y[t],x[0]==2,y[0]==4.5},{x[t],y[t]},t];
sol33=DSolve[{x'[t]==3*x[t]-2*y[t],y'[t]==2*x[t]-2*y[t],x[0]==-3,y[0]==-5.97},{x[t],y[t]},t];
trayectorias=ParametricPlot[{{sol11[[1,1,2]],sol11[[1,2,2]]},{sol22[[1,1,2]],sol22[[1,2,2]]},{sol33[[1,1,2]],sol33[[1,2,2]]}},{t,0,6},AxesLabel->{x,y},PlotRange->{{-4,4},{-4,4}},PlotStyle->Thick];
Show[{trayectorias,isoclinas,vectores}]