\[ y'(x)-\frac {\sqrt {\left | (1-y(x)) y(x) (1-a y(x))\right | }}{\sqrt {\left | (1-x) x (1-a x)\right | }}=0 \] ✗ Mathematica : cpu = 299.998 (sec), leaf count = 0 , timed out
$Aborted
✓ Maple : cpu = 0.077 (sec), leaf count = 139
\[ \left \{ -2\,{\frac {\sqrt {-ax+1}\sqrt {ax}}{a\sqrt {a{\it signum} \left ( x \left ( x-1 \right ) \left ( ax-1 \right ) \right ) {x}^{3}-{x}^{2}a{\it signum} \left ( x \left ( x-1 \right ) \left ( ax-1 \right ) \right ) -{\it signum} \left ( x \left ( x-1 \right ) \left ( ax-1 \right ) \right ) {x}^{2}+x{\it signum} \left ( x \left ( x-1 \right ) \left ( ax-1 \right ) \right ) }}\sqrt {-{\frac { \left ( x-1 \right ) a}{a-1}}}{\it EllipticF} \left ( \sqrt {-ax+1},\sqrt {- \left ( a-1 \right ) ^{-1}} \right ) }-\int ^{y \left ( x \right ) }\!{\frac {1}{\sqrt { \left | {\it \_a}\, \left ( {\it \_a}-1 \right ) \left ( {\it \_a}\,a-1 \right ) \right | }}}{d{\it \_a}}+{\it \_C1}=0 \right \} \]