\[ \boxed { 2\,x \left ( {x}^{2}-1 \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +2\, \left ( {x}^{2}-1 \right ) \left ( y \left ( x \right ) \right ) ^{2}- \left ( 3\,{x}^{2}-5 \right ) y \left ( x \right ) +{x}^{2}-3=0} \]
Mathematica: cpu = 0.068009 (sec), leaf count = 62 \[ \left \{\left \{y(x)\to \frac {\sqrt {x}}{\sqrt {1-x^2} \left (c_1-\frac {2 \sqrt {1-\frac {1}{x^2}} x F\left (\left .\sin ^{-1}\left (\frac {1}{\sqrt {x}}\right )\right |-1\right )}{\sqrt {1-x^2}}\right )}+1\right \}\right \} \]
Maple: cpu = 0.110 (sec), leaf count = 63 \[ \left \{ y \left ( x \right ) =1-2\,{\frac {\sqrt {x}}{\sqrt {x-1}\sqrt {1+x}} \left ( {\it \_C1}-2\,{\frac {{\it EllipticF} \left ( \sqrt {1+x} ,1/2\,\sqrt {2} \right ) \sqrt {-x}\sqrt {-2\,x+2}\sqrt {2}}{\sqrt {2\, x-2}\sqrt {x}}} \right ) ^{-1}} \right \} \]