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