Chapter 5: Differential Equation Graph Application 120
Graphing a Second Order Differential Equation
This section explains how to input a second order differential equation, draw a phase plane, and graph the
solution curve(s). With this application, a second order differential equation is input in the form of a set of two
first order differential equations.
• A phase plane is the family of solutions of either a second order differential equation or two first order
differential equations of the form x’ = dx/dt = f (x, y) and y’ = dy/dt = g(x, y). A single second order differential
equation can also be graphed, but it must be written as two first order differential equations.
• You can overlay, onto the phase plane, solution curves of the second order differential equation input on the
[DiffEq] tab for given initial conditions.
u To input a second order differential equation and draw a phase plane
0503 To input {x’ = x, y’ = −y} and draw its phase plane
u To input initial conditions and graph the solution curves
0504 After performing the operation under example 0503 , to graph the solution curve of the initial condition
(
xi, yi) = (1, 1)
Independent variable minimum value (tmin) = −7.7, maximum value (tmax) = 7.7, and initial value
(
t0) = 0
Graphing an Nth-order Differential Equation
This section explains how to graph the solution curve(s) for an nth-order (higher order) differential equation
based on specified initial conditions. With this application, an nth-order differential equation is input in the form
of a set of multiple first order differential equations.
Note: For nth-order differential equations, only solution curves are drawn.
u To input an nth-order differential equation and initial conditions, and then graph the solution
curves
0505 To specify the three initial conditions (xi, y1i, y2i) = (0, −1, 0), (0, 0, 0), (0, 1, 0) for the differential
equation y” = x − y, and graph its solution curves
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