Do asymptotic analysis for the following problem,

Question

I have an ordinary differential equation, $-\rho \frac{d\theta}{d\rho}=\frac{d}{d\rho}\left(\frac{\alpha^2}{(\beta+\theta)^2}\frac{d\theta}{d\rho}\right),$ where $\alpha$ and $\beta$ are parameters. How to do asymptotic analysis for $\theta(\rho)=\rho^{-a}(\log(\rho))^{b}$.