JSFHSystems of Differential Equations with MapleNote: You must always execute the following command first to get the Maple DE toolbox. Replace the colon by a semicolon and then press enter if you want to see all the commands that become available. Better yet, get Maple help on "DEtools".QyQtSSV3aXRoRzYiNiNJKERFdG9vbHNHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiUhIiI=Next, define the differential equations. Here are three interesting systems:Qyo+SSRERTFHNiI3JC8tSSVkaWZmRyUqcHJvdGVjdGVkRzYkLUkieEdGJTYjSSJ0R0YlRi8sJkYsIiIjLUkieUdGJUYuIiIiLy1GKTYkRjJGLywmRixGNEYyISIjRjQ+SSRERTJHRiU3JC9GKCwmRiwjISIiRjFGMkY0L0Y2LCZGLEZARjJGP0Y0PkkkREUzR0YlNyQvRigsJEYyRjkvRjYsJEYsI0Y0RjFGND5JJERFNEdGJTckL0YoKiZGLEY0LCgiIzlGNEYsRjlGMkZARjQvRjYqJkYyRjQsKCIjO0Y0RjJGOUYsRkBGNEY0print(); # input placeholderJSFHTime for a "phase plane" plot, replete with arrows, which also makes it a "direction field":
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%;
Next, we do a plot of the curves x(t):LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=QyQtSSdERXBsb3RHNiI2KUkkREUxR0YlNyQtSSJ4R0YlNiNJInRHRiUtSSJ5R0YlRisvRiw7IiIhIiImL0YqOyEjNSIjNTcoNyQvLUYqNiNGMSIiIi8tRi5GOyQiI0QhIiM3JEY5L0Y+IiIlNyRGOS9GPiEiJTckL0Y6ISIiRj03JEZJRkM3JEZJRkYvSSZzY2VuZUdGJTckRixGKS9JJ2Fycm93c0dGJUklbm9uZUdGJUY8%;JSFHNext, we do a plot of the curves y(t):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%;
Next, we do the nonlinear problem DE4, which is Example 1 of Section 6.1 in the text, p. 372:LUknREVwbG90RzYiNilJJERFNEdGJDckLUkieEdGJDYjSSJ0R0YkLUkieUdGJEYqL0YrOyIiISIjNS9GKTshIzVGMS9GLUYzNy03JC8tRik2I0YwIiIiLy1GLUY6Rjs3JEY4L0Y9IiIjNyRGOC9GPSIiJTckRjgvRj0iIic3JEY4L0Y9IiIpNyRGOC9GPUYxNyQvRjkkIiImISIiL0Y9JCIjdkZQNyRGTS9GPSRGTyEiIzckL0Y5RkkvRj1GTjckRllGPDckRlkvRj0iIiQvSSdhcnJvd3NHRiRJJ21lZGl1bUdGJA==%;JSFH