How do i get a direction field plot?

I need to get a direction field for this :

dx/dt = x(1.5 − x − 0.5y)

dy/dt = y(2 − y − 0.75x)

how would i do this?

Answer 1

[Durganshu]

Try this:

[x,y]=meshgrid(a:k:b, c:j:d)

meshgrid creates a set of points (x, y), where x lies between a and b, incremented by k, and y lies between c and d, incremented by j.

The given equation can be written like this:

y' = y*(2 − y − 0.75x) / (x*(1.5 − x − 0.5y))

dy = dt*y*(2 − y − 0.75*x);
dx = dt*x*(1.5 − x − 0.5*y);
quiver(a,b,x,y);

Now, quiver(a,b,x,y) begins at the point (a, b) and plots an arrow in the direction of the vector v = (x, y)

Afterwards, you can plot the graph.

Please refer to the following documentation for learning more on that:

https://in.mathworks.com/help/matlab/ref/meshgrid.html

https://in.mathworks.com/help/matlab/ref/quiver.html

https://www.math.tamu.edu/~efendiev/math442_spring04/matlabode.pdf

Hope that helps!!