Casio Differential Equation Software Manual

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[Page 1] Casio Differential Equation

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...

[Page 2] Casio Differential Equation

1-1 Using the DIFF EQ Mode 1. Using the DIFF EQ Mode You can solve differential equations numerically and graph the solutions. The general procedure for solving a differential equation is described below. Set Up 1. From the Main Menu, enter the DIFF ...

[Page 3] Casio Differential Equation

1-2 Using the DIFF EQ Mode 6. Specify variables to graph or to store in LIST. Press 5(SET) and select c(Output) to display the list setting screen. x, y, y (1) , y (2) , ....., y (8) stand for the independent variable, the dependent variable, the fi...

[Page 4] Casio Differential Equation

2-1 Differential Equations of the First Order 2. Differential Equations of the First Order k Separable Equation Description To solve a separable equation, simply input the equation and specify the initial values. dy/dx = f(x)g(y) Set Up 1. From the M...

[Page 5] Casio Differential Equation

2-2 Differential Equations of the First Order Example To graph the solutions of the separable equation dy/dx = y 2 –1, x0 = 0, y0 = {0, 1}, –5 << << < x << << < 5, h = 0.1. Use the following V-Window settings. Xmi...

[Page 6] Casio Differential Equation

2-3 Differential Equations of the First Order k Linear Equation To solve a linear equation, simply input the equation and specify initial values. dy/dx + f(x)y = g(x) Set Up 1. From the Main Menu, enter the DIFF EQ Mode. Execution 2. Press 1(1st) to ...

[Page 7] Casio Differential Equation

2-4 Differential Equations of the First Order Example To graph the solution of the linear equation dy/dx + xy = x, x0 = 0, y0 = –2, –5 << << < x << << < 5, h = 0.1. Use the following V-Window settings. Xmin = –6...

[Page 8] Casio Differential Equation

2-5 Differential Equations of the First Order k Bernoulli equation To solve a Bernoulli equation, simply input the equation and specify the power of y and the initial values. dy/dx + f(x)y = g(x)y n Set Up 1. From the Main Menu, enter the DIFF EQ M...

[Page 9] Casio Differential Equation

2-6 Differential Equations of the First Order Example To graph the solution of the Bernoulli equation dy/dx – 2y = –y 2 , x0 = 0, y0 = 1, –5 << << < x << << < 5, h = 0.1. Use the following V-Window settings. Xmin...

[Page 10] Casio Differential Equation

2-7 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 eq...

[Page 11] Casio Differential Equation

2-8 Differential Equations of the First Order Example To graph the solution of the first order differential equation dy/dx = –cos x, x0 = 0, y0 = 1, –5 << << < x << << < 5, h = 0.1. Use the following V-Window setti...

[Page 12] Casio Differential Equation

3-1 Linear Differential Equations of the Second Order 3. Linear Differential Equations of the Second Order Description To solve a linear differential equation of the second order, simply input the equation and specify the initial values. Slope fields...

[Page 13] Casio Differential Equation

3-2 Linear Differential Equations of the Second Order Example To graph the solution of the linear differential equation of the second order y앨 + 9y = sin 3x, x0 = 0, y0= 1, y쎾0 = 1, 0 << << < x << << < 10, h = 0.1....

[Page 14] Casio Differential Equation

4-1 Differential Equations of the Nth Order 4. Differential Equations of the Nth Order You can solve differential equations of the first through ninth order. The number of initial values required to solve the differential equation depends on its orde...

[Page 15] Casio Differential Equation

4-2 Differential Equations of the Nth Order Example To graph the solution of the differential equation of the fourth order below y (4) = 0, x0 = 0, y0 = 0, y쎾0 = –2, y앨0 = 0, y (3) 0 = 3, –5 << << < x << << <...

[Page 16] Casio Differential Equation

4-3 Differential Equations of the Nth Order k Converting a High-order Differential Equation to a System of the First Order Differential Equations You can convert a single N-th order differential equation to a system of n first order differential equa...

[Page 17] Casio Differential Equation

Example Express the differential equation below as a set of first order differential equations. y (3) = sinx – y쎾 – y앨, x0 = 0, y0 = 0, y쎾0 = 1, y앨0 = 0. Procedure 1 m DIFF EQ 2 3(N-th) 3 3(n)dw 4 sv-3(y(n)) b-3(y(n))cw 5aw aw bw aw 6 2(...

[Page 18] Casio Differential Equation

5. System of First Order Differential Equations A system of first order differential equations, for example, has dependent variables (y1), (y2), ....., and (y9), and independent variable x. The example below shows a system of first order differential...

[Page 19] Casio Differential Equation

Example 1 To graph the solution of first order differential equations with two unknowns below. (y1)쎾= (y2), (y2)쎾 = – (y1) + sin x, x0 = 0, (y1)0 = 1, (y2)0 = 0.1, –2 < x < 5, h = 0.1. Use the following V-Window settings. Xmin = –3, X...

[Page 20] Casio Differential Equation

Example 2 To graph the solution of the system of first order differential equations below. (y1)쎾 = (2 – (y2)) (y1) (y2)쎾 = (2 (y1) – 3) (y2) x0 = 0, (y1)0 = 1, (y2)0 = 1/4, 0 << << < x << << < 10, h = 0.1. Use ...

[Page 21] Casio Differential Equation

k Further Analysis To further analyze the result, we can graph the relation between (y1) and (y2). Procedure 1 m STAT 2 List 1, List 2, and List 3 contain values for x, (y1), and (y2), respectively. 3 1(GRPH)f(Set) 4 1(GPH1) 5 c2(xy) 6 c1(LIST)cw (XL...

[Page 22] Casio Differential Equation

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 clearl...