Differential Equations (DIFF EQ) Software for the ALGEBRA FX 2.0 1. Using the DIFF EQ Mode 2. Differential Equations of the First Order 3. Linear Differential Equations of the Second Order 4. Differential Equations of the Nth Order 5. System of First Order Differential Equations...
• With 1(1st), you need to make further selections of differential equation type. See “Differential equations of the first order” for more information. • With 3(N-th), you also need to specify the order of the differential equation, from 1 to 9.
Page 3
To specify a variable to store in LIST, select it using the cursor keys (f, c) and press 2(LIST). 7. Press !K(V-Window) to display the V-Window setting screen. Before you solve a differential equation, you need to make V-Window settings. Xmin … -axis minimum value max …...
6. Specify the calculation range. 7. Specify the step size for 8. Press 5(SET)c(Output). Select the variable you want to graph, and then select a list for storage of the calculation results. 9. Make V-Window settings. 10. Press 6(CALC) to solve the differential equation.
Page 5
Differential Equations of the First Order Example To graph the solutions of the separable equation = {0, 1}, –5 < < < < < = 0, Use the following V-Window settings. Xmin = –6.2, Xmax = 6.2, Xscale = 1 Ymin = –3.1, Ymax = 3.1, Yscale = 1 Procedure 1 m DIFF EQ...
Page 6
6. Specify the calculation range. 7. Specify the step size for 8. Press 5(SET)c(Output). Select the variable you want to graph, and then select a list for storage of the calculation results. 9. Make V-Window settings. 10. Press 6(CALC) to solve the differential equation.
Page 7
Differential Equations of the First Order Example To graph the solution of the linear equation = –2, –5 < < < < < = 0, Use the following V-Window settings. Xmin = –6.2, Xmax = 6.2, Xscale = 1 Ymin = –3.1, Ymax = 3.1, Yscale = 1 Procedure 1 m DIFF EQ 2 1(1st)c(Linear)
Page 8
7. Specify the step size for 8. Press 5(SET)c(Output). Select the variable you want to graph, and then select a list for storage of the calculation results. 9. Make V-Window settings. 10. Press 6(CALC) to solve the differential equation. and the...
Page 9
Differential Equations of the First Order Example To graph the solution of the Bernoulli equation = 1, –5 < < < < < = 0, Use the following V-Window settings. Xmin = –6.2, Xmax = 6.2, Xscale = 1 Ymin = –3.1, Ymax = 3.1, Yscale = 1 Procedure 1 m DIFF EQ 2 1(1st)d(Bern)
Page 10
Differential Equations of the First Order k Others To solve a general differential equation of the first order, simply input the equation and specify the initial values. Use the same procedures as those described above for typical differential equations of the first order.
Page 11
Differential Equations of the First Order Example To graph the solution of the first order differential equation = – cos Use the following V-Window settings. Xmin = –6.2, Xmax = 6.2, Xscale = 1 Ymin = –3.1, Ymax = 3.1, Yscale = 1...
Order Description To solve a linear differential equation of the second order, simply input the equation and specify the initial values. Slope fields are not displayed for a linear differential equation of the second order. Set Up 1. From the Main Menu, enter the DIFF EQ Mode.
Page 13
Linear Differential Equations of the Second Order Example To graph the solution of the linear differential equation of the second order = sin 3 Use the following V-Window settings. Xmin = –1, Xmax = 11, Ymin = –3.1, Ymax = 3.1, Yscale = 1...
)i(Y8) ... 3( )j(Y9) k Differential Equation of the Fourth Order The following example shows how to solve a differential equation of the fourth order. , ... , Set Up 1. From the Main Menu, enter the DIFF EQ Mode.
Page 15
Differential Equations of the Nth Order Example To graph the solution of the differential equation of the fourth order below = 0, = 0, Use the following V-Window settings. Xmin = –6.2, Xmax = 6.2, Xscale = 1 Ymin = –3.1, Ymax = 3.1, Yscale = 1...
Page 16
Y3 (3( 5. Specify the initial value for 6. Press 2( SYS). 7. Press w(Yes). • The entered differential equation is converted to a system of three first order differential equations. Initial values are also converted accordingly. , and first order...
Page 17
3 3( 4 sv-3( ) b-3( 5 aw 6 2( SYS) 7 w(Yes) The differential equation is converted to a set of first order differential equations as shown below. )n = )n = )n = sin – ( ) – (...
System of First Order Differential Equations 5. System of First Order Differential Equations A system of first order differential equations, for example, has dependent variables ( ..., and ( ), and independent variable differential equations. )n= ( )n= – ( ) + sin Set Up 1.
Page 19
System of First Order Differential Equations Example 1 To graph the solution of first order differential equations with two unknowns below. )n= ( ), ( )n = – ( Use the following V-Window settings. Xmin = –3, Xmax = 6, Ymin = –2, Ymax = 2, Procedure...
Page 20
System of First Order Differential Equations Example 2 To graph the solution of the system of first order differential equations below. )n = (2 – ( )) ( )n = (2 ( ) – 3) ( = 0, ( = 1, ( Use the following V-Window settings.
Page 21
System of First Order Differential Equations k Further Analysis To further analyze the result, we can graph the relation between ( Procedure 1 m STAT 2 List 1, List 2, and List 3 contain values ), and ( ), respectively. 3 1(GRPH)f(Set) 4 1(GPH1) 5 c2(...
Page 22
System of First Order Differential Equations Important! • This calculator may abort calculation part way through when an overflow occurs part way through the calculation when calculated solutions cause the solution curve to extend into a discontinuous region, when a calculated value is clearly false, etc. •...