# 1. Differential Equation[-]

The function $${\rm arccot} \left( x \right)$$ satisfies the differential equation$$\displaystyle \left( {x}^{2}+1 \right) {\frac {d^{2}}{d{x}^{2}}}y \left( x \right) +2\,x{\frac {d}{dx}}y \left( x \right) = 0$$ with initial values $$y \left( 0 \right) =\frac{\pi }{2}$$ and $$y' \left( 0 \right) =-1$$.

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

The differential equation above has 2 non-zero finite .