Given $$\vec {P} = \alpha \vec {r}$$, where $$\vec {r} =$$ distance from the axis. The space density of charges is given by, $$\rho' = -div \vec {P} = -2\alpha$$
On using. $$\div \vec {r} = \dfrac {1}{r} \dfrac {\partial}{\partial r} (\vec {r} . \vec {r}) = 2$$.