- #1

fluidistic

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## Homework Statement

Find all the critical points of the system of DE:

[itex]x'=x-x^2-2xy[/itex] and [itex]y'=2y-2y^2-3xy[/itex].

## Homework Equations

[itex]y'=f(x, \vec y)[/itex] has critical point if [itex]f(\vec x )=0[/itex].

## The Attempt at a Solution

I'm self studying DE's and I'm not understanding well what critical points are.

It looks like I must equate x' to 0 and isolate x (which I've done and it gave me [itex]x=0[/itex] or [itex]x=1-2y[/itex]) and equal y' to 0 and isolate y, which I've done and got [itex]y=0[/itex] or [itex]y=1-\frac{3x}{2}[/itex].

Now I don't know what to do.