# 1. Differential Equation[-]

The function $${\rm arcsec} \left( x \right)$$ satisfies the differential equation$$\displaystyle \left( {x}^{2}-1 \right) x{\frac {d^{2}}{d{x}^{2}}}y \left( x \right) + \left( 2\,{x}^{2}-1 \right) {\frac {d}{dx}}y \left( x \right) = 0.$$

# 5. Local Expansions at Singularities and at Infinity[-]

The differential equation above has 2 non-zero finite .