\[ y''(x)=-\frac {3 y(x)}{16 (x-1)^2 x^2} \] ✓ Mathematica : cpu = 0.0414975 (sec), leaf count = 51
\[\left \{\left \{y(x)\to \frac {2 c_2 (1-x)^{3/4} x^{5/4}}{\sqrt {-(x-1) x}}+c_1 (1-x)^{3/4} \sqrt [4]{x}\right \}\right \}\] ✓ Maple : cpu = 0.042 (sec), leaf count = 25
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{x}^{{\frac {3}{4}}}\sqrt [4]{x-1}+{\it \_C2}\,\sqrt [4]{x} \left ( x-1 \right ) ^{{\frac {3}{4}}} \right \} \]