- #1

Phys pilot

- 25

- 0

## Homework Statement

I have to calculate the critical points of the following system.

$$x'=cx+10x^2$$

$$y'=x-2y$$

## The Attempt at a Solution

So I solve the system

$$cx+10x^2=0$$

$$x-2y=0$$

So if $$x=2y$$ I have $$2yc+10*4y^2=2yc+40y^2=y(2c+40y)=0$$ and I get $$y=0$$ and $$y=-\frac{c}{20}$$ f I substitute in $$x=2y$$ I get $$x=0$$ and $$x=-\frac{c}{10}$$

Then we have that the critical points are $$(0,0)$$ and $$(-\frac{c}{10},-\frac{c}{20})$$

Is this correct? I don't know if the procedure to get the critical points is like this.

Thanks