How do I get phase section of this equation?

the equation is

y=dx/dt

dy/dt=-0.05y-sin(x)+0.7 cos(wt)

w is given 0.1, 0.2, 0.3... to 1.5

I can't set any equation as both equations are contataing both variables, and I want to get the graph of x and y

Answer 1

[Ameer Hamza]

Try this

W = 0.1:0.1:1.5;
odefun = @(t,X,w) [X(2); -0.05*X(2)-sin(X(1))+0.7*cos(w*t)];

t = 0:0.1:10;
ic = [0;0];
X_sol = cell(1,numel(W));
for i=1:numel(W)
    [~, X_sol{i}] = ode45(@(t,X) odefun(t, X, W(i)), t, ic);
end

tiledlayout('flow')
for i=1:numel(X_sol)
    nexttile
    plot(X_sol{i}(:,1), X_sol{i}(:,2));
    xlabel('x')
    ylabel('y')
    title(['w = ' num2str(W(i))]);
end

The tiledlayout will work for R2019b and onward. For older versions using the following lines to plot the figure

figure;
for i=1:numel(X_sol)
    subplot(4,4,i);
    plot(X_sol{i}(:,1), X_sol{i}(:,2));
    xlabel('x')
    ylabel('y')
    title(['w = ' num2str(W(i))]);
end