\[ y'(x)=\frac {x^3 \sqrt {4 a x-y(x)^2}+x^2 \sqrt {4 a x-y(x)^2}+\sqrt {4 a x-y(x)^2}+2 a}{y(x)} \] ✓ Mathematica : cpu = 2.73291 (sec), leaf count = 145
\[\left \{\left \{y(x)\to -\frac {1}{12} \sqrt {576 a x-9 x^8-24 x^7-16 x^6-72 x^5-96 x^4-72 c_1 x^4-96 c_1 x^3-144 x^2-288 c_1 x-144 c_1{}^2}\right \},\left \{y(x)\to \frac {1}{12} \sqrt {576 a x-9 x^8-24 x^7-16 x^6-72 x^5-96 x^4-72 c_1 x^4-96 c_1 x^3-144 x^2-288 c_1 x-144 c_1{}^2}\right \}\right \}\] ✓ Maple : cpu = 0.359 (sec), leaf count = 35
\[-\sqrt {-y \relax (x )^{2}+4 a x}-\frac {x^{4}}{4}-\frac {x^{3}}{3}-x -c_{1} = 0\]