Question

MMatlab Please

Homework Due Nov. 19 1. Solve the ODE system (Van der Pol's equation) below using the function ode45 and the initial values y,0) = y20) = 1. dyi at = 32 wat = u(1 – y})yz – yı where u = 1 and solve between t = 0 to 20. dt Hint: for this equation, your initial conditions yo will have 2 values. For the odefun, you will have a one output, two inputs (t and y), and the equations arranged as: output = [y(2); 1 * (1 - y(1)) * y(2) – y(1)]

Answer 1

MATLAB Script:

close all
clear
clc

tspan = [0 20];
y0 = [1 1]; % Initial conditions [y1(0) y2(0)]
[t, y] = ode45(@(t, y) odefcn(t, y), tspan, y0); % Solve the system
plot(t, y(:,1), '-', t, y(:,2), '-.')
legend('y_1(t)', 'y_2(t)', 'Location', 'northwest')
title('Solution of Vander Pol''s Equation')
xlabel('t'), ylabel('y(t)')

function dydt = odefcn(t, y)
mu = 1;
dydt = [y(2); mu*(1 - y(1)^2)*y(2) - y(1)];
end

Plot:

Solution of Vander Pol's Equation 3 y, (t) --Y2(t) 1 -3 6 8 10 12 14 16 18 20 CO (1)A