How do I plot a direction field for x'=y and y'=-sinx?

I have tried:

[x,y] = meshgrid(-5,5:-5,5);
x=-5:.1:5;
y=-sin(x);
u=x;
v=y;
quiver(x,y,u,v)

[Dyuman Joshi]

"x'=y and y'=-sinx"

What does this mean? Are those differential equations?

Also, you initialize x and y using meshgrid, but you over-write them in the next lines. Which values are the correct ones?

[Sophie]

I need to plot a direction field for the given planar autonomous system, and those are the equations for the system. I do not really know how to use matlab so I'm not sure which values are the correct one? I think what I was supposed to do is create a new variable when inputting the actual equation part?

Answer 1

[Taylor]

% Define the range of x and y values
x = linspace(-pi, pi, 20);
y = linspace(-2, 2, 20);

% Create a grid of x and y values
[X, Y] = meshgrid(x, y);

% Calculate the derivatives dx/dt and dy/dt
dXdt = Y;
dYdt = -sin(X);

% Plot the direction field
quiver(X, Y, dXdt, dYdt);
xlabel('x');
ylabel('y');
title('Direction Field');

% Adjust the aspect ratio and grid
axis tight;
grid on;

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