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20060301
14-3-1
Graphing a Second Order Differential Equation
14-3 Graphing a Second Order Differential
Equation
This section explains how to input a second order differential equation and draw a slope
field, and how to graph the solution curve(s) for a second order differential equation based
on given initial conditions.
With this application, a second order differential equation is input in the form of a set of two
first order differential equations.
Drawing the Phase Plane of a Second Order Differential Equation
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.
Example: To input {
x
’ =
x
,
y
’ = −
y
} and draw its phase plane
S
ClassPad 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] - [2nd (Phase Plane)] or the
toolbar button.
(3) Use the differential equation editor to input
x
’ =
x
,
y
’ = −
y
.
7
U
8
U
- ClassPad 330 1
- FCC WARNING 2
- Declaration of Conformity 2
- Getting Ready 3
- ClassPad 5
- 3. Using the Stylus 5
- 5. User Registration 8
- Handling Precautions 9
- 2006030120080201 10
- Contents 12
- 2006030120070301 25
- About This User’s Guide 26
- 1-1 General Guide 30
- 1-6 Input 51
- 1-7 Variables and Folders 70
- 20060301 100
- Chapter 109
- 20090601 111
- 2-2 Basic Calculations 116
- 2-4 Function Calculations 128
- 2-5 List Calculations 146
- 2-7 Specifying a Number Base 156
- 2-8 Using the Action Menu 161
- with Other Applications 222
- 2-11 Using Verify 233
- 2-12 Using Probability 237
- 20070301 247
- 3-2 Using the Graph Window 257
- 3-3 Storing Functions 268
- 3-4 Using Table & Graph 282
- 3-5 Modifying a Graph 297
- 3-6 Using the Sketch Menu 303
- 3-7 Using Trace 308
- 4-2 Inputting Equations 327
- 4-3 Drawing a Conics Graph 330
- 5-2 Inputting an Expression 349
- 5-3 Drawing a 3D Graph 351
- 20080201 352
- Application 369
- 6-4 Using LinkTrace 376
- 6-5 Drawing a Cobweb Diagram 377
- 7-2 Using Stat Editor 383
- • MSe = 411
- ClassPad Operation 413
- Residual Calculation 418
- Calculations 420
- Example 2: Two-Way ANOVA 422
- 7-9 Tests 424
- 1-Sample 425
- 2-Sample 427
- Linear Regression 435
- 7-10 Confidence Intervals 443
- Interval 444
- Distribution Command List 455
- Normal Probability Density 455
- Student 458
- Probability Density 458
- Cumulative Distribution 459
- Inverse 462
- = p(1– p) 472
- Edit Menu 484
- File Menu 484
- View Menu 485
- Draw Menu 485
- Tap i and then tap a figure 486
- Do this: 486
- To do this: 486
- 8-2 Drawing Figures 487
- 8-3 Editing Figures 531
- 8-5 Working with Animations 549
- Applications 557
- Numeric Solver window 569
- Graph Editor window 569
- 9-2 Using Numeric Solver 570
- Insert Menu 576
- Action Menu 576
- Other Buttons 577
- 10-2 Creating an eActivity 579
- Using the Presentation 606
- 11-2 Building a Presentation 611
- Entering the Editing Mode 619
- Editing Operations 621
- Using the Program 629
- Editor window 633
- Program Application Overview 633
- 12-2 Creating a New Program 637
- “CAUTION” file 640
- Local Variables 644
- 12-3 Debugging a Program 646
- 12-4 Managing Files 651
- 12-5 User-defined Functions 653
- Program Command Reference 657
- { } 664
- Using the Spreadsheet 708
- 13-4 Editing Cell Contents 719
- 13-6 Statistical Calculations 753
- 13-9 Graphing 778
- Using the Differential 799
- Equation Graph 799
- Overview 800
- Equation 813
- View Window Parameters 820
- Operations 823
- Using the Financial 833
- 15-2 Simple Interest 841
- Calculation Formulas 842
- 15-3 Compound Interest 843
- { } 845
- 15-4 Cash Flow 846
- 15-5 Amortization 850
- 15-6 Interest Conversion 854
- 15-7 Cost/Sell/Margin 856
- 15-8 Day Count 857
- 15-9 Depreciation 859
- 15-10 Bond Calculation 863
- Issue date 866
- Redemption date (d2) 866
- 15-11 Break-Even Point 868
- 15-12 Margin of Safety 871
- 15-13 Operating Leverage 872
- 15-14 Financial Leverage 873
- 15-15 Combined Leverage 874
- 15-16 Quantity Conversion 875
- Configuring System 877
- Settings 877
- 16-1 System Setting Overview 878
- 16-2 Managing Memory Usage 880
- Deleting Memory Usage Data 882
- Arrangement 890
- 16-10 Optimizing “Flash ROM” 891
- Imaginary Unit 896
- Hard Keys 897
- How to Transfer Data 902
- Selecting Data for Transfer 911
- Appendix 915
- 2 Deleting an Application 918
- 5 Specifications 925
- 6 Character Code Table 927
- 2002080120060301 928
- 8 Command and Function Index 938
- Statistical - Plot 946
- 10 Error Message Table 948
- CASIO COMPUTER CO., LTD 954
- 6-2, Hon-machi 1-chome 954
- U.S.Pats. 5,539,867 954
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