\[ y''(x)=-\frac {3 y(x)}{16 (x-1)^2 x^2} \] ✓ Mathematica : cpu = 0.0454112 (sec), leaf count = 49
\[\left \{\left \{y(x)\to \frac {(1-x)^{3/4} \sqrt [4]{x} \left (c_1 \sqrt {-(x-1) x}+2 c_2 x\right )}{\sqrt {-(x-1) x}}\right \}\right \}\]
✓ Maple : cpu = 0.038 (sec), leaf count = 25
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,\sqrt [4]{x-1}{x}^{{\frac {3}{4}}}+{\it \_C2}\, \left ( x-1 \right ) ^{{\frac {3}{4}}}\sqrt [4]{x} \right \} \]