Slope Field

In calculus applications, one may be asked to construct the slope field for a given basic differential equation, then display the solution trajectory for a given initial condition. We illustrate with an exponential growth example. Suppose an organism grows according to the differential equation y' = .08y where y(0) = 10.

To view the slope field, first we need to set the graph mode to differential equations. Press to access the mode menu. Highlight the Graph mode (FUNCTION is showing in the window displayed below). Press the right arrow key on the thumb pad to display the Graph menu. Select 6:DIFF EQUATIONS, then press . Finally, press again to save the mode settings.

Press to enter the equation editor. Enter the differential equation, y1' = .08*y1, then press . Press to access the Zoom menu, then select 6:ZoomStd to view a slope field. For a better view, press WINDOW to access the window menu. The slope field below at right uses the window settings xmin = 0, xmax = 50, xscl = 10, ymin = 0, ymax = 100, yscl = 10. Then press GRAPH to view the slope field.

To view a trajectory determined by an initial condition, press to return to the equation editor. Enter yi1 = 10 (initial condition), then press . Then press GRAPH to view the slope field with the solution curve.

Warning Remember to set the Graph mode back to function for doing usual calculator work.