PLEASE USE MATLAB TO AND SHOW THE CODING TO Solve Example 6.2 on page 111 of textbook, using (1) the 4^th order Runge Kutta method and (2) Simulink method, respectively.

You can use the results from the code attached below (from the textbook by ODE45 solver) as a reference.

Example 6.2 ode45 ex.m % This program solves a system of 3 differential equations % by using ode45 function % y1 (O)-0, y2 (0)=1.0, y3 (O)-1.0 clear; clc initial=[0. O 1.0 1.0]; tspan 0.0:0.1:10.0 options-odeset ('RelTol',1.0e-6, 'AbsTol', [1.0e-6 1.0e-6 1.0e-6]) [t, Y] =ode 45 ( @dyat3 , tspan, initial , options) ; disp (P) yl-P(,2) y2-P(,3) y3-P(:,4); fid-fopen ('output.txt' , 'w') fprintf (fid,' fprintf (fid, for i=1:2:101 y (2) y(3) ' fprintf (fid,' %6.2f %10.2f %10.2f 10.2n',. . . end fclose (fid) plot (t1,Y(: ,1),tl,Y(:, 2),' -. ',tl,Y(: ,3),', xlabel('t' ylabel ('Y(1), Y (2),Y (3)),title ('Y vs. t') grid text (6.0, -1.2, 'y(l)'),text (7.7, -0.25, 'y(2)), text (4.2,0.85,'y(3)' % dydt3.m % functions for example problem function Yprime-dydt3 (t,Y) Yprime-zeros (3,1); Yprime (1)-Y (2) Y (3) *t Yprime (2)Y (1) Y (3) Yprime (3)0.51*Y (1) Y (2) Example 6.2 ode45 ex.m % This program solves a system of 3 differential equations % by using ode45 function % y1 (O)-0, y2 (0)=1.0, y3 (O)-1.0 clear; clc initial=[0. O 1.0 1.0]; tspan 0.0:0.1:10.0 options-odeset ('RelTol',1.0e-6, 'AbsTol', [1.0e-6 1.0e-6 1.0e-6]) [t, Y] =ode 45 ( @dyat3 , tspan, initial , options) ; disp (P) yl-P(,2) y2-P(,3) y3-P(:,4); fid-fopen ('output.txt' , 'w') fprintf (fid,' fprintf (fid, for i=1:2:101 y (2) y(3) ' fprintf (fid,' %6.2f %10.2f %10.2f 10.2n',. . . end fclose (fid) plot (t1,Y(: ,1),tl,Y(:, 2),' -. ',tl,Y(: ,3),', xlabel('t' ylabel ('Y(1), Y (2),Y (3)),title ('Y vs. t') grid text (6.0, -1.2, 'y(l)'),text (7.7, -0.25, 'y(2)), text (4.2,0.85,'y(3)' % dydt3.m % functions for example problem function Yprime-dydt3 (t,Y) Yprime-zeros (3,1); Yprime (1)-Y (2) Y (3) *t Yprime (2)Y (1) Y (3) Yprime (3)0.51*Y (1) Y (2)