\[ y'(x)-\frac {\sqrt {| (1-y(x)) y(x) (1-a y(x))| }}{\sqrt {| (1-x) x (1-a x)| }}=0 \] ✓ Mathematica : cpu = 0.212899 (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 = 0.258 (sec), leaf count = 40
\[\left \{c_{1}-\left (\int _{}^{y \left (x \right )}\frac {1}{\sqrt {{| \left (\textit {\_a} -1\right ) \left (\textit {\_a} a -1\right ) \textit {\_a} |}}}d \textit {\_a} \right )+\int \frac {1}{\sqrt {{| \left (x -1\right ) \left (a x -1\right ) x |}}}d x = 0\right \}\]