\[ y'(x)-\frac {\sqrt {| (1-y(x)) y(x) (1-a y(x))| }}{\sqrt {| (1-x) x (1-a x)| }}=0 \] ✓ Mathematica : cpu = 0.152548 (sec), leaf count = 67
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{\sqrt {| (1-K[1]) K[1] (1-a K[1])| }}dK[1]\& \right ]\left [\int _1^x\frac {1}{\sqrt {| (1-K[2]) K[2] (1-a K[2])| }}dK[2]+c_1\right ]\right \}\right \}\] ✓ Maple : cpu = 0.089 (sec), leaf count = 40
\[ \left \{ \int \!{\frac {1}{\sqrt { \left | x \left ( x-1 \right ) \left ( ax-1 \right ) \right | }}}\,{\rm d}x-\int ^{y \left ( x \right ) }\!{\frac {1}{\sqrt { \left | {\it \_a}\, \left ( {\it \_a}-1 \right ) \left ( {\it \_a}\,a-1 \right ) \right | }}}{d{\it \_a}}+{\it \_C1}=0 \right \} \]