\[ y'(x)-\frac {\sqrt {| (1-y(x)) y(x) (1-a y(x))| }}{\sqrt {| (1-x) x (1-a x)| }}=0 \] ✓ Mathematica : cpu = 0.174545 (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 = 0.233 (sec), leaf count = 40
\[\int \frac {1}{\sqrt {{| x \left (x -1\right ) \left (a x -1\right )|}}}d x -\left (\int _{}^{y \relax (x )}\frac {1}{\sqrt {{| \textit {\_a} \left (\textit {\_a} -1\right ) \left (\textit {\_a} a -1\right )|}}}d \textit {\_a} \right )+c_{1} = 0\]