How can I plot the vector field of a differential equation on the real line?

Hello,

I´m trying to plot

https://scielo.conicyt.cl/fbpe/img/rchnat/v77n4/FIG2pag715.jpg

for the differential equation x'=4x^2-16

[darova]

You want vectorfield or solution(curve)?

[Amy]

No I dont´t want the solution(curve). I need the vector field on the real line. I just want the arrows only at the positions of the root, indicating if the function has a positive or negative derivative at the root as shown in the example.

[darova]

What about quiver?

[Amy]

I´ve tried that but I can´t manage to get the arrows just at the roots. Maybe you can help me with that.

[Amy]

I don´t know what to choose for u an v in quiver(x,y,u,v).

Answer 1

[darova]

I reached some success. Look, it should me heplpfull

clc,clear

[X,Y] = meshgrid(-2:0.2:2);
F = @(X,Y) 4*Y.^2 - 16;
[x,y] = ode45(F,[-2 2],2-1e-4);
DY = F(1,Y);
DX = DY*0+1;

cla
h1 = quiver(X,Y,DX,DY);
h2 = streamline(X,Y,DX,DY,-2:2,1.9*ones(1,5));
set(h2,'color','g')
hold on
h3 = plot(x,y,'r');
hold off

legend([h1 h2(1) h3],'quiver','streamline','ode45 solution')

[Amy]

thanks this looks great. But I just need the vectors at the roots. So I´ve tried plotting f(x)=4x^2-16 and then inserting the arrows via annotation. The problem is that the vector isn´t located where I want it to be.

[darova]

Locate vector where you want

quiver(x,0,1,0)

[Amy]

It doesn´t work. :(

[darova]

Try this

[x,y] = ode45(F,[-2 2],2-1e-4);
x1 = linspace(x(1),x(end),10);
y1 = interp1(x,y,x1);
quiver(x1,x1*0,abs(y1)./y1,x1*0,0.2)

[Diego]

i do