# Exercise on dynamical system

using this phase portrait :

a)When $t=0$ we have that $x=0$ and $y=0.25$

If $(x(t),y(t))$ is the solution satisfying the initial previous conditions what is the approximate value of $y(t)$ when $x(t)=0$

\begin{align} y\approx -2 & ~~\text{or}~~ y\approx -1 \\ & ~~\text{or}~~y\approx 0\\ y\approx 1 & ~~\text{or}~~\text{ we can not answer}~~ \end{align}

b) we suppose that $t=-2$ we have that $x=-2$ and $y=-0,25$ ,can we give an approximate value of $y$ on $t=0$ ? if yes what is it ?

I have no idea how to solve this exercise , can someone help me ?

Sketch the locus of the solution by following the arrows. For a) you are given one solution at $t=0$, that is, $y=0.25$. Roughly drawing the solution from the initial point suggests the other intersection is around $y=1.75$. None of the alternatives seems correct. For b), the phase portrait has no time information so I have no idea how you are supposed to solve this. –  copper.hat Sep 19 '13 at 16:22
Draw a dot at $(0, 0.25)$, then 'follow the arrows'. –  copper.hat Sep 19 '13 at 16:32