\[ y''(x)=-\frac {y(x) \left (b x^2+c x+d\right )}{a (x-1)^2 x^2} \] ✓ Mathematica : cpu = 11.6066 (sec), leaf count = 413606
DSolve[Derivative[2][y][x] == -(((d + c*x + b*x^2)*y[x])/(a*(-1 + x)^2*x^2)),y[x],x]
\[ \text {Too large to display} \] ✓ Maple : cpu = 0.122 (sec), leaf count = 272
dsolve(diff(diff(y(x),x),x) = -(b*x^2+c*x+d)/a/x^2/(x-1)^2*y(x),y(x))
\[y \left (x \right ) = \left (x -1\right )^{-\frac {\sqrt {a -4 b -4 c -4 d}-\sqrt {a}}{2 \sqrt {a}}} \left (\hypergeom \left (\left [-\frac {\sqrt {a -4 b -4 c -4 d}-\sqrt {a}-\sqrt {a -4 d}+\sqrt {a -4 b}}{2 \sqrt {a}}, \frac {-\sqrt {a -4 b -4 c -4 d}+\sqrt {a}+\sqrt {a -4 d}+\sqrt {a -4 b}}{2 \sqrt {a}}\right ], \left [\frac {\sqrt {a}+\sqrt {a -4 d}}{\sqrt {a}}\right ], x\right ) x^{\frac {\sqrt {a}+\sqrt {a -4 d}}{2 \sqrt {a}}} c_{1}+x^{\frac {\sqrt {a}-\sqrt {a -4 d}}{2 \sqrt {a}}} \hypergeom \left (\left [-\frac {\sqrt {a -4 b -4 c -4 d}-\sqrt {a}+\sqrt {a -4 d}+\sqrt {a -4 b}}{2 \sqrt {a}}, -\frac {\sqrt {a -4 b -4 c -4 d}-\sqrt {a}+\sqrt {a -4 d}-\sqrt {a -4 b}}{2 \sqrt {a}}\right ], \left [\frac {\sqrt {a}-\sqrt {a -4 d}}{\sqrt {a}}\right ], x\right ) c_{2}\right )\]