# System Help

1. Dec 10, 2004

### MrBioMedic

Hello everyone I am hoping to get a little with a system.

Here is the the system:

dx = y
dt

dy = -y^2 - sin(x)
dt

I need to find all the equilibira and determine whether they are sinks, sources, etc...

I need to sketch the x and y nullclines.

Indicate the direction of the solution curve in any regions bounded by the nullcines.

Lastly, sketch the entire phase plane.

Thank you for the help in advance!

2. Dec 11, 2004

### arildno

What have you done so far?

3. Dec 11, 2004

### HallsofIvy

Staff Emeritus
An "equilibrium" point is where the function is a constant: you must have
$$\frac{dx}{dt}= y= 0$$
and
$$/frac{dy}{dt}= -y^2- sin9x)= 0$$.

What does that tell you?

Last edited: Dec 11, 2004