\[ y'(x)=\frac {\left (4 a x-y(x)^2\right )^3}{y(x) \left (4 a x-y(x)^2-1\right )} \] ✓ Mathematica : cpu = 0.363625 (sec), leaf count = 89
\[\text {Solve}\left [2 a \left (x-\frac {\text {RootSum}\left [-\text {$\#$1}^3+2 \text {$\#$1} a-2 a\& ,\frac {\text {$\#$1} a \log \left (-\text {$\#$1}+4 a x-y(x)^2\right )-a \log \left (-\text {$\#$1}+4 a x-y(x)^2\right )}{2 a-3 \text {$\#$1}^2}\& \right ]}{2 a}\right )=c_1,y(x)\right ]\] ✓ Maple : cpu = 1095.87 (sec), leaf count = 229
\[\int _{\textit {\_b}}^{x}-\frac {\left (4 \textit {\_a} a -y \relax (x )^{2}\right )^{3}}{-y \relax (x )^{6}+12 \textit {\_a} a y \relax (x )^{4}+\left (-48 \textit {\_a}^{2} a^{2}+2 a \right ) y \relax (x )^{2}+64 \textit {\_a}^{3} a^{3}-8 \textit {\_a} \,a^{2}+2 a}d \textit {\_a} +\int _{}^{y \relax (x )}\left (\frac {\left (-\textit {\_f}^{2}+4 a x -1\right ) \textit {\_f}}{-\textit {\_f}^{6}+12 \textit {\_f}^{4} a x -48 \textit {\_f}^{2} a^{2} x^{2}+64 a^{3} x^{3}+2 \textit {\_f}^{2} a -8 a^{2} x +2 a}-\left (\int _{\textit {\_b}}^{x}-\frac {4 \left (4 \textit {\_a} a -\textit {\_f}^{2}\right )^{2} \textit {\_f} a \left (8 \textit {\_a} a -2 \textit {\_f}^{2}-3\right )}{\left (64 \textit {\_a}^{3} a^{3}-48 \textit {\_a}^{2} \textit {\_f}^{2} a^{2}+12 \textit {\_a} \,\textit {\_f}^{4} a -\textit {\_f}^{6}-8 \textit {\_a} \,a^{2}+2 \textit {\_f}^{2} a +2 a \right )^{2}}d \textit {\_a} \right )\right )d \textit {\_f} +c_{1} = 0\]