[x,y] = meshgrid(-3:0.2:4,-3:0.2:4);
n=size(x);
u = ones(n);
v = 1-x.*y.^2;

for i = 1:numel(x)
rac = 2*sqrt(u(i)^2 + v(i)^2);
u(i) = u(i)/rac;
v(i) = v(i)/rac;
end

xspan = [-2 3];
x0 = -2;
[xx,yy] = ode45(@(x,y) 1-x*y^2, xspan, x0);

figure
hold on
quiver(x,y,u,v)
plot(xx,yy,'-')
