\[ y''(x)=-\frac {3 y(x)}{16 (x-1)^2 x^2} \] ✓ Mathematica : cpu = 0.0230288 (sec), leaf count = 41
DSolve[Derivative[2][y][x] == (-3*y[x])/(16*(-1 + x)^2*x^2),y[x],x]
\[\left \{\left \{y(x)\to 2 c_2 \sqrt [4]{1-x} x^{3/4}+c_1 (1-x)^{3/4} \sqrt [4]{x}\right \}\right \}\] ✓ Maple : cpu = 0.026 (sec), leaf count = 25
dsolve(diff(diff(y(x),x),x) = -3/16/x^2/(x-1)^2*y(x),y(x))
\[y \left (x \right ) = c_{1} \left (x -1\right )^{\frac {1}{4}} x^{\frac {3}{4}}+c_{2} \left (x -1\right )^{\frac {3}{4}} x^{\frac {1}{4}}\]