\[ \boxed { \left ( {x}^{2}+1 \right ) {\frac {{\rm d}^{3}}{{\rm d}{x}^{3}}}y \left ( x \right ) +8\,x{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) +10\,{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -3+{x}^{-2}-2\,\ln \left ( x \right ) =0} \]
Mathematica: cpu = 0.106013 (sec), leaf count = 62 \[ \left \{\left \{y(x)\to c_3-\frac {100 \left (3 c_2-1\right ) x^3+900 c_2 x+225 c_1+36 x^5-60 \left (3 x^4+10 x^2+15\right ) x \log (x)}{900 \left (x^2+1\right )^2}\right \}\right \} \]
Maple: cpu = 0.031 (sec), leaf count = 86 \[ \left \{ y \left ( x \right ) ={\frac {{x}^{2} \left ( {x}^{2}+2 \right ) {\it \_C1}}{ \left ( {x}^{2}+1 \right ) ^{2}}}+{\frac {x \left ( {x}^{2}+ 3 \right ) {\it \_C2}}{ \left ( {x}^{2}+1 \right ) ^{2}}}+{\frac {{\it \_C3}}{ \left ( {x}^{2}+1 \right ) ^{2}}}+{\frac {x \left ( 45\,{x}^{4} \ln \left ( x \right ) -9\,{x}^{4}+150\,{x}^{2}\ln \left ( x \right ) - 50\,{x}^{2}+225\,\ln \left ( x \right ) -225 \right ) }{225\, \left ( {x} ^{2}+1 \right ) ^{2}}} \right \} \]