The TI-89 has a built-in function called "deSolve" that allows you to graph ODE integral curves. Simply input your differential equation and the initial conditions, and the graph will be generated.
Yes, you can graph multiple integral curves on the same graph by using the "deSolve" function multiple times, each with different initial conditions. You can also use the "Parametric" function to graph multiple integral curves at once.
You can change the range of the x and y-axis on the graph by pressing the "Window" button on your TI-89. From there, you can adjust the minimum and maximum values for the x and y-axis to better fit your integral curves.
Yes, you can save your graph by pressing the "F3" button on your TI-89 and selecting "Save Graph". You can then give your graph a name and it will be saved in the "Graphs" folder.
While the TI-89 is a powerful tool for graphing integral curves, there are some limitations. It may not be able to graph extremely complex or large systems of ODEs, and it may not be as accurate as using more advanced software programs.