\[ y''(x)=\frac {(x-4) y'(x)}{2 (x-2) x}-\frac {(x-3) y(x)}{2 (x-2) x^2} \] ✓ Mathematica : cpu = 0.0453433 (sec), leaf count = 41
\[\left \{\left \{y(x)\to \frac {\sqrt [4]{x-2} \sqrt {x} \left (2 c_2 \sqrt {x-2}+c_1\right )}{\sqrt [4]{2-x}}\right \}\right \}\]
✓ Maple : cpu = 0.035 (sec), leaf count = 19
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,\sqrt {x}+{\it \_C2}\,\sqrt {x \left ( x-2 \right ) } \right \} \]