Graphing a First Order Differential Equation
14-2 Graphing a First Order Differential Equation
This section explains how to input a first order differential equation and draw a slope field, and how to graph the solution curve(s) of a first order differential equation based on given initial conditions.
Inputting a First Order Differential Equation and Drawing a Slope FieldA slope field is the family of solutions of a single, first order differential equation of the form
y’= f(x, y). It is a grid of solution lines where each line has the slope y’ for a given grid value of x and y. It is often referred to as a “slope field” or “direction field” because only the direction of the field at any given point in known, not the magnitude.
Example: To input y’ = y2 − x and draw its slope field
uClassPad Operation
(1)On the application menu, tap .
•This starts up the Differential Equation Graph application and activates the differential equation editor ([DiffEq] tab).
(2)Tap [Type] - [1st (Slope Field)] or the Atoolbar button.
(3)Press the kkey to display the soft keyboard.
(4)Input y’ = y2 − x.
20060301