\[ y''(x)=\frac {(x-4) y'(x)}{2 (x-2) x}-\frac {(x-3) y(x)}{2 (x-2) x^2} \] ✓ Mathematica : cpu = 0.0314324 (sec), leaf count = 55
\[\left \{\left \{y(x)\to \frac {c_1 \sqrt [4]{x-2} \sqrt {x}}{\sqrt [4]{2-x}}+\frac {2 c_2 (x-2)^{3/4} \sqrt {x}}{\sqrt [4]{2-x}}\right \}\right \}\] ✓ Maple : cpu = 0.02 (sec), leaf count = 19
\[y \relax (x ) = c_{1} \sqrt {x}+c_{2} \sqrt {x \left (x -2\right )}\]