Dynamical Systems -- pages 312--313

Problem 1.  x'(t) = 0*x(t) + 1*y(t), y'(t) = -4*x(t) + 0*y(t).

VectorPlot[{y,-4x},{x,-2,2},{y,-2,2},Axes->True,VectorScale->{Small,Automatic,None},AxesLabel->{"x","y"}]

StreamPlot[{y,-4x},{x,-2,2},{y,-2,2},Axes->True,StreamScale->{Small,Automatic,None},AxesLabel->{"x","y"}]

Quit[]

Problem 3.  x'(t) = 2*x(t) + 1*y(t),   y'(t) = 1*x(t) + 2*y(t).

VectorPlot[{2x+y, x + 2y},{x,-2,2},{y,-2,2},Axes->True,VectorScale->{Small,Automatic,None},AxesLabel->{"x","y"}]

StreamPlot[{2x+y, x + 2y},{x,-2,2},{y,-2,2},Axes->True,StreamScale->{Small,Automatic,None},AxesLabel->{"x","y"}]

Problem 5.  x'(t) = 3*x(t) - 1*y(t), y'(t) = 1*x(t) + 2*y(t).

VectorPlot[{3x-y,x  + 2y},{x,-2,2},{y,-2,2},Axes->True,VectorScale->{Small,Automatic,None},AxesLabel->{"x","y"}]

StreamPlot[{3x-y,x  + 2y},{x,-2,2},{y,-2,2},Axes->True,StreamScale->{Small,Automatic,None},AxesLabel->{"x","y"}]

Problem 7.    x'(t) = x(t),  y'(t) = x(t) +  2y(t)

VectorPlot[{x, x + 2y},{x,-2,2},{y,-2,2},Axes->True,VectorScale->{Small,Automatic,None},AxesLabel->{"x","y"}]

StreamPlot[{x, x + 2y},{x,-2,2},{y,-2,2},Axes->True,StreamScale->{Small,Automatic,None},AxesLabel->{"x","y"}]

Problem 13.  x'(t) = -5x(t) - 4y(t),  y'(t) = 2x(t) + y(t).

VectorPlot[{-5x - 4y, 2x + y}, {x,-2,2},{y,-2,2},Axes->True,VectorScale->{Small,Automatic,None},AxesLabel->{"x","y"}]

StreamPlot[{-5x - 4y, 2x + y},{x,-2,2},{y,-2,2},Axes->True,StreamScale->{Small,Automatic,None},AxesLabel->{"x","y"}]

Problem 15.  x'(t) = y(t),  y'(t) = 2x(t) + y(t).

VectorPlot[{y, 2x + y}, {x,-2,2},{y,-2,2},Axes->True,VectorScale->{Small,Automatic,None},AxesLabel->{"x","y"}]

StreamPlot[{y, 2x + y},{x,-2,2},{y,-2,2},Axes->True,StreamScale->{Small,Automatic,None},AxesLabel->{"x","y"}]

Problem 17.  x'(t) = - 5x - y,  y'(t) = 3x - y.

VectorPlot[{-5x - y, 3x - y}, {x,-2,2},{y,-2,2},Axes->True,VectorScale->{Small,Automatic,None},AxesLabel->{"x","y"}]

StreamPlot[{-5x - y, 3x - y},{x,-2,2},{y,-2,2},Axes->True,StreamScale->{Small,Automatic,None},AxesLabel->{"x","y"}]

Problem 21.  x'(t) = 4x + 3y,  y'(t) = 3x + 4y.

VectorPlot[{4x + 3y,  3x + 4y}, {x,-2,2},{y,-2,2},Axes->True,VectorScale->{Small,Automatic,None},AxesLabel->{"x","y"}]

StreamPlot[{4x + 3y,  3x + 4y},{x,-2,2},{y,-2,2},Axes->True,StreamScale->{Small,Automatic,None},AxesLabel->{"x","y"}]