Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 305 / 4 / a / i / Solution

Separating variables givesThereforeFor $b>0$, define the strong-coupling scaleThenIt decreases logarithmically toward zero in the ultraviolet and grows toward the infrared, becoming nonperturbative when $\mu$ approaches ${\Lambda }_{\mathrm{QCD}}$.