\[ y'(x)-\frac {\sqrt {\left | (1-y(x)) y(x) (1-a y(x))\right | }}{\sqrt {\left | (1-x) x (1-a x)\right | }}=0 \] ✓ Mathematica : cpu = 755.428 (sec), leaf count = 65
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}} \frac {1}{\sqrt {\left | (1-K[1]) K[1] (1-a K[1])\right | }} \, dK[1]\& \right ]\left [\int _1^x \frac {1}{\sqrt {\left | (1-K[2]) K[2] (1-a K[2])\right | }} \, dK[2]+c_1\right ]\right \}\right \}\] ✓ Maple : cpu = 0.178 (sec), leaf count = 40
\[ \left \{ \int \!{\frac {1}{\sqrt { \left | x \left ( x-1 \right ) \left ( ax-1 \right ) \right | }}}\,{\rm d}x-\int ^{y \left ( x \right ) }\!{\frac {1}{\sqrt { \left | {\it \_a}\, \left ( {\it \_a}-1 \right ) \left ( {\it \_a}\,a-1 \right ) \right | }}}{d{\it \_a}}+{\it \_C1}=0 \right \} \]