Question

Differential Equations with MATLAB/Plotting first order differential equations in Matlab/ Differential Equations MATLAB/IVP Matlab/IVP

I'd really appreciate if I can get some help plotting these 3 first order differential equations as well as their comments. PLEASE! ANYTHING HELPS, I am very stuck :(

EZplot and ODE 45 were mentioned in class and the instructions in class were not clear at all.

Given the first order differential equation with initial condition. dy/dt = y t, y(0)=-1 Complete problems 1-3 in one M-file with comment: 1) Make a conjecture about the long term behavior of the solution function. Do not use technology to make this conjecture. 2) Plot the solution curve through the given initial condition on the window t:[0,4], y:[ -4,4]. 3) Does your plot verify your conjecture? If not, why do you think you didn't guess correctly? Make a second conjecture if the initial conditions change to y(0) = 1. 4) Suppose you are given these two first order differential equations with initial conditions: DE 2: dy/dt = -0.08y²+0.8y, y(0) = 1 DE 3: dy/dt = y’cos(t), y(0) = 1 Make a second and third conjecture about the long term behavior of each - not using technology. 5) Verify your conjectures from (4) graphically and analytically using only MATLAB m-files as follows: • Complete 4 and 5 with DE2 in a second M-file with comment. • Complete 4 and 5 with DE3 in a third M-file with comment.

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,y) -0.08*y^2+0.8*y;
[T,Y]=ode45(f,[0,4],1);
plot(T,Y);
xlabel('t');
ylabel('y(t)');
title('Plot of DE2');
figure;
f=@(t,y) y^2*cos(t);
[T,Y]=ode45(f,[0,4],1);
plot(T,Y);
xlabel('t');
ylabel('y(t)');
title('Plot of DE3');

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Kindly revert for any queries

Thanks.