\[ y'(x)=\frac {a^3 x^3 y(x)^3+3 a^2 x^2 y(x)^2+a^2 x y(x)+a^2 x+3 a x y(x)+a+1}{a^2 x^2 (a x y(x)+a x+1)} \] ✓ Mathematica : cpu = 0.241931 (sec), leaf count = 106
\[\left \{\left \{y(x)\to -\frac {a x+1}{a x}+\frac {1}{a^3 x^3 \left (\frac {1}{a^3 x^3}-\frac {1}{x^3 \sqrt {-2 a^6 x+c_1}}\right )}\right \},\left \{y(x)\to -\frac {a x+1}{a x}+\frac {1}{a^3 x^3 \left (\frac {1}{a^3 x^3}+\frac {1}{x^3 \sqrt {-2 a^6 x+c_1}}\right )}\right \}\right \}\] ✓ Maple : cpu = 0.047 (sec), leaf count = 72
\[y \relax (x ) = \frac {a x -\sqrt {c_{1}-2 x}+1}{a x \left (\sqrt {c_{1}-2 x}-1\right )}\]