Question

i need help writing the matlab code for this!

2. The fourth order differential equation 2.(4) + 3.0" – sin(t)..' + 8x = {2 can be rewritten as the following system of first order equations Ti = 12 = 13 24 = -8.01 + sin(t). 2- 3.03 + t (a) Write an m-file function for the system of differential equations. (1) Solve the system of equations over the interval ( € (0,25) for the initial conditions 21(0) = 1, 12(0) = 2, 23(0) = 3, 04(0) = 4. (c) Plot the component curve solutions found in (b). The 21(t), 32(t), 23(t), 24(t) curves should be plotted on one graph together against t. Use a legend to distinguish the curves and be sure to label the axes of the plot. (d) Plot the phase-plane solution for 22 and 23 in the 22.03-plane. That is, plot the 23 solution vector against the 22 solution vector. Label the axes of the plot.

Answer 1

`Hey,

Note: Brother if you have any queries related the answer please do comment. I would be very happy to resolve all your queries.

clc

clear all

close all

f=@(t,x) [x(2);x(3);x(4);-8*x(1)+sin(t)*x(2)-3*x(3)+t^2];

[T,X]=ode45(f,[0,25],[1,2,3,4]);

plot(T,X);

legend('x1(t)','x2(t)','x3(t)','x4(t)');

figure;

plot(X(:,2),X(:,3));

xlabel("x_2");

ylabel('x_3');

title("Plot on x2 x3 plane");

Kindly revert for any queries

Thanks.