How do I get this plot in Matlab?

I am trying to get this particular plot from this general solution from the files attached.

I have some initial code and I understand that my general solution is wrongly types and I am trying to do it without the quiver function in Matlab is that possible?

Code 1:

% Define the general solution
X_general = @(c1, c2) [c1 * (2 - 1) * exp(-t)+ c2 * (1 2) * exp(-6 * t)]

Invalid expression. Check for missing multiplication operator, missing or unbalanced delimiters, or other syntax error. To construct matrices, use brackets instead of parentheses.

y=-x/2;
xlabel('x');
ylabel('y');
% Substitute the values of c1 and c2 based on your calculations
c1 = 1/5;
c2 = 3/5;
hold on;
%plot([c1 * (2 - 1) * exp(-t)+ c2 * (1/2) * exp(-6 * t)], 'b-', 'LineWidth', 2, 'DisplayName', 'X(1)');
plot(y)

I plotted against time for code 2 to test out quiver:
t = linspace(0, 5, 20);

% Define the general solution
X_general = @(t, c1, c2) [c1 * (2 - 1) * exp(-t); c2 * (1/2) * exp(-6 * t)]

% Substitute the values of c1 and c2 based on your calculations
c1 = 1/5;
c2 = 3/5;

% Evaluate the solution for the given time vector
X_values_general = X_general(t, c1, c2);

% Create a meshgrid for the quiver plot
[T, C] = meshgrid(t, linspace(0, 5, 20));

% Evaluate the derivatives
dXdt = zeros(size(T));
dXdt(:, :, 1) = (2 - 1) * C * exp(-T);
dXdt(:, :, 2) = (1/2) * C * exp(-6 * T);

% Create a quiver plot
figure;
quiver(T, C, dXdt(:, :, 1), dXdt(:, :, 2), 'AutoScale', 'on', 'LineWidth', 1.5);
xlabel('Time');
ylabel('Constant Value');
title('Quiver Plot of the Vector Field');

% Overlay the trajectory
hold on;
plot(t, c1 * (2 - 1) * exp(-t), 'b-', 'LineWidth', 2, 'DisplayName', 'X(1)');
plot(t, c2 * (1/2) * exp(-6 * t), 'r-', 'LineWidth', 2, 'DisplayName', 'X(2)');
legend('Vector Field', 'X(1)', 'X(2)');

Answer 1

[Chunru]

% Define the general solution
% [2 -1] and [1 2] are vectors.  Use [ ].
X_general = @(t, c1, c2) (c1 * [2 -1] .* exp(-t)+ c2 * [1 2] .* exp(-6 * t))

X_general = function_handle with value:
    @(t,c1,c2)(c1*[2,-1].*exp(-t)+c2*[1,2].*exp(-6*t))

t = linspace(0, 5, 20)';   % make this as column verctor

% Substitute the values of c1 and c2 based on your calculations
c1 = 1/5;
c2 = 3/5;
% Evaluate the solution for the given time vector
X_values_general = X_general(t, c1, c2);
% Create a meshgrid for the quiver plot
[T, C] = meshgrid(t, linspace(0, 5, 20));
% Evaluate the derivatives
dXdt = zeros(size(T));
dXdt(:, :, 1) = (2 - 1) * C * exp(-T);
dXdt(:, :, 2) = (1/2) * C * exp(-6 * T);
% Create a quiver plot
figure;
quiver(T, C, dXdt(:, :, 1), dXdt(:, :, 2), 'AutoScale', 'on', 'LineWidth', 1.5);
xlabel('Time');
ylabel('Constant Value');
title('Quiver Plot of the Vector Field');
% Overlay the trajectory
hold on;
plot(t, c1 * (2 - 1) * exp(-t), 'b-', 'LineWidth', 2, 'DisplayName', 'X(1)');
plot(t, c2 * (1/2) * exp(-6 * t), 'r-', 'LineWidth', 2, 'DisplayName', 'X(2)');
legend('Vector Field', 'X(1)', 'X(2)');

[Yeen Kit Lee]

Thanks I can't believe i forgot to use [] for vectors! Let me try this out thank you for helping.

[Yeen Kit Lee]

Im trying to get as close to this image as possible, let me try to figure out how to mess with the code and if there's anything else I will post another thread thank you.