Question

Hey guys,

I would like to solve these equations using ode45 in MATLAB

QUESTION 1)

QUESTION 2)

where k and c are:

For a better understanding of how these values came about:

I deeply appreciate your assistance to these guys.

Thanks

b2-1.ば2-('22'2-v211. 2'2(0)=220 predator 2'2 dr2 cr1 +k(t)), 12_ x2(to) =y0. := k(t) kle fes ya Building Spring/ Damper Wheel Axle Tires Street

Answer 1

Question 1)

MATLAB code is given below in bold letters.

clc;
close all;
clear all;

% define the time range
t = 0:0.1:5;

% define the initial conditions
x0 = [1 ; 1];

[t,y] = ode45(@vdp1,t,x0);

% Plot the solutions fot y(t) and ydot(t) against t.
figure;plot(t,y(:,1),'-o',t,y(:,2),'-o')
title('Solution of Equation with ODE45');grid;
xlabel('Time t');
ylabel('Solution x1(t) and x2(t)');
legend('x1','x2')

function dydt = vdp1(t,x)
% inpuut
u = ones(size(t));

% Assume the constants
a1 = 1;
b1 = 1;
c1 = 1;
v1 = 1;

b2 = 1;
c2 = 1;
v2 = 1;

% Define the derivatives of the states ydot(t)
dydt = [a1*x(1)-b1*x(1)*x(2)-c1*x(1)-v1*u; b2*x(1)*x(2)-c2*x(2)-v2*u];

The result is plotted below

Solution of Equation with ODE45 듦 -3 び) -6 -7 0 0.5 11.5 2 2.5 33.5 4.5 5 Time t -8

Question 2)

MATLAB code is given below in bold letters.

clc;
close all;
clear all;

% define the time range
t = 0:0.1:10;

% define the initial conditions
x0 = [1 ; 1];

[t,y] = ode45(@vdp1,t,x0);

% Plot the solutions fot y(t) and ydot(t) against t.
figure;plot(t,y(:,1),'-o',t,y(:,2),'-o')
title('Solution of Equation with ODE45');grid;
xlabel('Time t');
ylabel('Solution x1(t) and x2(t)');
legend('x1','x2');

function dydt = vdp1(t,x)
% inpuut
k = ones(size(t));

% Assume the constants
d = 1;
c = 1;
k = 1;
m = 1;

% Define the derivatives of the states ydot(t)
dydt = [x(2);1/m*(-d*x(2)-c*x(1)+k)];

The result is plotted below

Solution of Equation with ODE45 1.6 CN 0.81 e 0.4 0.2 -0.2 0 1 234 5 6 78 910 Time t 0.4