Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 218 / 2 / c / Solution

Writing the horizontal coordinate as $u=\log \lambda$, so that $\lambda =e^u$, the two coefficient paths at $\alpha =1/2$ areEquivalently, as functions of $\lambda$, replace every $e^u$ by $\lambda$. The paths reach zero at $lambda=2.82$ and $lambda=0.82$, respectively.