Blowing-up a singular point

I have this system of ODEs:

$$x’=-y+ \mu x(x^2+y^2)$$

$$y’=x+ \mu y(x^2+y^2)$$

I already find that in $\mathbb{R}^2$ the only singular point is $(0,0)$. So I have to blow-up the singularity to find the phase diagram. For that I use polar coordinates, the problem is that I get a system of the form

$$r’=\mu r^3$$

so $\theta’$ is never zero, but I’m pretty sure that the system has at least 2 singular points, any ideas about how to solve this problem?

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