User manual CASIO DIFFERENTIAL EQUATION SOFTWARE GUIDE

[. . . ] · 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. · With 4(SYS), you also need to specify the number of unknowns, from 1 to 9. [. . . ] Press 6(CALC) to solve the differential equation. 2-2 Differential Equations of the First Order Example Procedure 1 m DIFF EQ 2 1(1st)b(Separ) 3 bw a-(Y)Mc-bw 4 aw !*( { )a, b!/( } )w 5 5(SET)b(Param) 6 -fw fw 7 a. bwi 8 5(SET)c(Output)4(INIT)i 9 !K(V-Window) -g. cw g. cw bwc -d. bw d. bw bwi 0 6(CALC) Result Screen # To graph a family of solutions, enter a list of initial conditions. To graph the solutions of the separable equation dy/dx = y2 ­1, x0 = 0, y0 = {0, 1}, ­5 < x < 5, h = 0. 1. Xmin = ­6. 2, Xmax = 6. 2, Xscale = 1 Ymin = ­3. 1, Ymax = 3. 1, Yscale = 1 (x0, y0) = (0, 1) (x0, y0) = (0, 0) 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 display the menu of differential equations of the first order, and then select c(Linear). Select the variable you want to graph, and then select a list for storage of the calculation results. Press 6(CALC) to solve the differential equation. 2-4 Differential Equations of the First Order Example Procedure 1 m DIFF EQ 2 1(1st)c(Linear) 3 vw vw 4 aw -cw 5 5(SET)b(Param) 6 -fw fw 7 a. bwi 8 5(SET)c(Output)4(INIT)i 9 !K(V-Window) -g. cw g. cw bwc -d. bw d. bw bwi 0 6(CALC) Result Screen To graph the solution of the linear equation dy/dx + xy = x, x0 = 0, y0 = ­2, ­5 < x < 5, h = 0. 1. Xmin = ­6. 2, Xmax = 6. 2, Xscale = 1 Ymin = ­3. 1, Ymax = 3. 1, Yscale = 1 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. From the Main Menu, enter the DIFF EQ Mode. Execution 2. Press 1(1st) to display the menu of differential equations of the first order, and then select d(Bern). Select the variable you want to graph, and then select a list for storage of the calculation results. Press 6(CALC) to solve the differential equation. 2-6 Differential Equations of the First Order Example Procedure 1 m DIFF EQ 2 1(1st)d(Bern) 3 -cw -bw cw 4 aw bw 5 5(SET)b(Param) 6 -fw fw 7 a. bwi 8 5(SET)c(Output)4(INIT)i 9 !K(V-Window) -g. cw g. cw bwc -d. bw d. bw bwi 0 6(CALC) Result Screen To graph the solution of the Bernoulli equation dy/dx ­ 2y = ­y2, x0 = 0, y0 = 1, ­5 < x < 5, h = 0. 1. Xmin = ­6. 2, Xmax = 6. 2, Xscale = 1 Ymin = ­3. 1, Ymax = 3. 1, Yscale = 1 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 equations of the first order. dy/dx = f(x, y) Set Up 1. From the Main Menu, enter the DIFF EQ Mode. Execution 2. Press 1(1st) to display the menu of differential equations of the first order, and then select e(Others). Select the variable you want to graph, and then select a list for storage of the calculation results. Press 6(CALC) to solve the differential equation. 2-8 Differential Equations of the First Order Example Procedure 1 m DIFF EQ 2 1(1st)e(Others) 3 -cvw 4 aw bw 5 5(SET)b(Param) 6 -fw fw 7 a. bwi 8 5(SET)c(Output)4(INIT)i 9 !K(V-Window) -g. cw g. cw bwc -d. bw d. bw bwi 0 6(CALC) Result Screen To graph the solution of the first order differential equation dy/dx = ­ cos x, x0 = 0, y0 = 1, ­5 < x < 5, h = 0. 1. Xmin = ­6. 2, Xmax = 6. 2, Xscale = 1 Ymin = ­3. 1, Ymax = 3. 1, Yscale = 1 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 are not displayed for a linear differential equation of the second order. y + f(x) yn + g(x)y = h(x) Set Up 1. From the Main Menu, enter the DIFF EQ Mode. Execution 2. Specify the initial value for x0, y0, yn0. [. . . ] In other cases, reduce the size of the calculation range and the value of h (step size) and try again. When you need to perform a calculation using a very wide calculation range, store intermediate results in a list and perform a new calculation starting from step 3 using the stored results as initial values. You can repeat this step multiple times, if necessary. k SET UP Items G-Mem {G-Mem 20}/{1 ­ 20} . . . . . . Specifies a memory location {G-Mem No. } for storage of the latest graph functions. [. . . ]