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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 ' =
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 { ' = , ' = − } and draw its phase plane
u To input initial conditions and graph the solution curves
0504
After performing the operation under example
( ,
) = (1, 1)
Independent variable minimum value ( min) = −7.7, maximum value ( max) = 7.7, and initial value
( 0) = 0
Graphing an Nth-order Differential Equation
This section explains how to graph the solution curve(s) for an th-order (higher order) differential equation
based on specified initial conditions. With this application, an th-order differential equation is input in the form
of a set of multiple first order differential equations.
Note:
For th-order differential equations, only solution curves are drawn.
u To input an
n
th-order differential equation and initial conditions, and then graph the solution
curves
0505
To specify the three initial conditions ( , 1 , 2 ) = (0, −1, 0), (0, 0, 0), (0, 1, 0) for the differential
equation " = − , and graph its solution curves
/
= ( , ) and ' =
0503
, to graph the solution curve of the initial condition
Chapter 5: Differential Equation Graph Application
/
= ( , ). A single second order differential
120
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