Cartesian to Polar coordinates where alpha is real parameter

Question

I want to convert the following equation in Cartesian form to Polar:

$$-y(1+\alpha+x)+x(1-x^2-y^2)$$

so $x = r\cos(\theta)$ and $y = r\sin(\theta)$

I can get this far: $$r\cos(\theta)(1-r^2)-r\sin(\theta)(1+\alpha+r\cos(\theta))$$

But the answer should be: $$r(1-r^2)$$

What am I doing wrong?

Answer 1

Nothing is wrong. The answer clearly should depend on $\alpha$. The only way the answer you showed can be correct is if one takes $\theta$ to be $0$.