Direction Fields Plotting Direction fields can be done using the function quiver quiver Quiver plot. quiver (X,Y,U,V) plots velocity vectors as arrows with components (u,v) at the points (xy). The matrices X,Y,U,V must all be the same size and contain corresponding position and velocity components (X and Y can also be vectors to specify a uniform grid), quiver automatically scales the arrows to fit within the grid. Example: xrange = -5:0.5:5; %the domain of x is from -5 up to 5 with 8.5 interval. yrange -10:1:10; %the values of y is from -10 up to 10 with 1 interval. [x,y] = meshgrid(xrange,yrange); %plot the DE y = x^2+y^2; S = x.^2+y^2; quiver (x,y,ones (size(s)),s) Exercises: Sketch the direction fields of the following differential equations 1. y' = 0.25xy² 2. y' = sin(x-y) Notes: For the ranges: For Item No.1 Use xr1 = (-5,5) with 0.5 interval yr1 = (-10,10) with 0.5 interval Use $1 for the f(x,y), x1 and y1 as the points in the rectangular coordinate system, For Item No.2 Use xr2 = (-10,10) with 1 interval yr2 = (-6,6) with 0.2 interval Use s2 for the f(x,y), x2 and y2 as the points in the rectangular coordinate system,