\[ y'(x)=\frac {x \sqrt {4 a x-y(x)^2}+2 a}{y(x)} \] ✓ Mathematica : cpu = 1.15176 (sec), leaf count = 101
\[\left \{\left \{y(x)\to -\frac {\sqrt {4096 a^5 x-256 a^4 x^4+32 a^2 e^{c_1} x^2-e^{2 c_1}}}{32 a^2}\right \},\left \{y(x)\to \frac {\sqrt {4096 a^5 x-256 a^4 x^4+32 a^2 e^{c_1} x^2-e^{2 c_1}}}{32 a^2}\right \}\right \}\] ✓ Maple : cpu = 0.221 (sec), leaf count = 27
\[-\sqrt {-y \relax (x )^{2}+4 a x}-\frac {x^{2}}{2}-c_{1} = 0\]