\begin{array}{rcl}Y<a&\Leftrightarrow&\frac{2X}{1-X^2}<a,
\vspace{0.5em}\\ &\Leftrightarrow&
2X<a(1-X^2),
\vspace{0.5em}\\ &\Leftrightarrow&
aX^2+2X-a<0.