Past exam of the mathematics course of the year 2 of the natural sciences course of the University of Cambridge / 2007 / Paper 1 / 6 / i

Put $s=z-1$ and seek the leading Frobenius series term $y\sim s^{\rho }$. The coefficients of $y^{\prime \prime }$ and $y^{\prime }$ become $-2s(1+s)$ and $2+s$, respectively. The lowest power, $s^{\rho -1}$, therefore has coefficient $-2\rho (\rho -1)+2\rho$. The indicial equation isThe term $-y$ contributes only at the next order and does not enter this equation.