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