\[ y'(x)=\frac {1}{2} \sqrt {a} \left (2 \sqrt {a x^4+8 y(x)}-\sqrt {a} x^3+2 x^3 \sqrt {a x^4+8 y(x)}+2 x^2 \sqrt {a x^4+8 y(x)}\right ) \] ✓ Mathematica : cpu = 0.56267 (sec), leaf count = 93
\[\left \{\left \{y(x)\to \frac {144 a x^8+384 a x^7+256 a x^6+1152 a x^5+1464 a x^4-1152 a c_1 x^4+96 a x^3-1536 a c_1 x^3+2304 a x^2+288 a x-4608 a c_1 x+9 a+2304 a c_1{}^2-288 a c_1}{1152}\right \}\right \}\] ✓ Maple : cpu = 0.593 (sec), leaf count = 40
\[\frac {\sqrt {a \,x^{4}+8 y \relax (x )}}{4}+\frac {\left (-3 x^{4}-4 x^{3}-12 x \right ) \sqrt {a}}{12}-c_{1} = 0\]