How do I construct matrices of multiple variables and plot a graph

I am a beginner to MATLAB.

I tried but I'm getting errors.

Anybody, kindly help. Thank you.

Equations dx/dt=-2x

dy/dt=2x

Initial condition: x(t=0)=100

y(t=0)=0

tspan=[0 3];
x0=100;
y0=0;
dzdt = (dxdt dydt);

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

[tSol, zSol]=ode45(@odefun,tspan,x0);
plot(tSol, zSol);

function dzdt=odefun(t,z)
    x = z(1);
    y = z(2);
    dxdt = -2*x;
    dydt = 2*x;
    dzdt = [dxdt;dydt];
end 

Answer 1

[Hassaan]

% Define the time span and initial conditions
tspan = [0 3];
z0 = [100; 0];  % Initial conditions for x and y, combined into a single column vector

% Call the ODE solver
[tSol, zSol] = ode45(@odefun, tspan, z0);

% Plot the solutions for x and y over time
figure; % Open a new figure window
hold on; % Keep the plot for adding both x and y
plot(tSol, zSol(:,1), 'b-', 'LineWidth', 2); % Plot x with a thicker blue line
plot(tSol, zSol(:,2), 'r--', 'LineWidth', 2); % Plot y with a thicker red dashed line
xlabel('Time t', 'FontSize', 12, 'FontWeight', 'bold');
ylabel('Solutions x and y', 'FontSize', 12, 'FontWeight', 'bold');
title('Solutions to the differential equations dx/dt = -2x and dy/dt = 2x', 'FontSize', 14, 'FontWeight', 'bold');
legend('x(t)', 'y(t)');
grid on; % Turn on grid
set(gca, 'FontSize', 10); % Set the font size for axes
hold off; % Release the plot hold

% Define the system of differential equations
function dzdt = odefun(t, z)
    x = z(1);
    y = z(2);
    dxdt = -2 * x;
    dydt = 2 * x;
    dzdt = [dxdt; dydt];
end

[Alfred]

Thank you very much @Hassaan. Your answer is helpful.

[Hassaan]

@Alfred You are welcome.

[Alfred]

How do I find the maximum value of x?

How do I find the value of x at y=2?

@Hassaan@Torsten

I saw a code about interpolation, so I just edited it. However, I don't know if it is the right code for the question, and I don't even understand it. Kindly assist me. Thank you.

tspan=[0 3];
x0=100;
y0=0;
z0=[x0;y0];
[tSol, zSol]=ode45(@odefun,tspan,z0);


function dzdt=odefun(t,z)
    x = z(1);
    y = z(2);
    dxdt = -2*x;
    dydt = 2*x;
    dzdt = [dxdt;dydt];
end 


plot(tSol, zSol);

% Finding the time at which the maximum value occured

zmax=max(zSol);

tmaz = interp1(tSol,zSol,zmax);

% Find max value over all elements.
maxz = max(zSol)

maxz = 1x2

100.0000 99.7521

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% Get first element that is the max.
indexOfFirstMax = find(zSol == maxz, 1, 'first') 

indexOfFirstMax = 1

% Get the x and y values at that index.
maxt = tSol(indexOfFirstMax)

maxt = 0

maxX = zSol(indexOfFirstMax)

maxX = 100

[Torsten]

tspan=[0 3];
x0=100;
y0=0;
z0=[x0;y0];
[tSol, zSol]=ode45(@odefun,tspan,z0);

function dzdt=odefun(t,z)
    x = z(1);
    y = z(2);
    dxdt = -2*x;
    dydt = 2*x;
    dzdt = [dxdt;dydt];
end 

How do I find the maximum value of x?

xmax = max(zSol(:,1))

xmax = 100

How do I find the value of x at y=2?

t2 = interp1(zSol(:,2),tSol,2);   % find time at which y = 2
x2 = interp1(tSol,zSol(:,1),t2)   % find x at which time = time at which y = 2

x2 = 98

[Alfred]

Thank you @Torsten

[Alfred]

How do I find the maximum value of x?

xmax = max(zSol(:,1))

What is the meaning of the "1" in the code?

@Torsten

[Torsten]

zSol has two columns: the first is x over time, the second is y over time.

[Alfred]

okay. Thank you

Answer 2

[Torsten]

tspan=[0 3];
x0=100;
y0=0;
z0=[x0;y0];
[tSol, zSol]=ode45(@odefun,tspan,z0);
plot(tSol, zSol);

function dzdt=odefun(t,z)
    x = z(1);
    y = z(2);
    dxdt = -2*x;
    dydt = 2*x;
    dzdt = [dxdt;dydt];
end 

[Alfred]

Thank you very much @Torsten. Your answer is helpful