\[ x^5 (-\log (x))+x^2 y''(x)-2 x y'(x)+2 y(x)=0 \] ✓ Mathematica : cpu = 0.024225 (sec), leaf count = 32
\[\left \{\left \{y(x)\to c_2 x^2+c_1 x-\frac {7 x^5}{144}+\frac {1}{12} x^5 \log (x)\right \}\right \}\]
✓ Maple : cpu = 0.047 (sec), leaf count = 25
\[ \left \{ y \left ( x \right ) ={\frac {{x}^{5}\ln \left ( x \right ) }{12}}-{\frac {7\,{x}^{5}}{144}}+{x}^{2}{\it \_C2}+{\it \_C1}\,x \right \} \]