\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac { \left ( - \left ( y \left ( x \right ) \right ) ^{2}+4\,ax \right ) ^{3}}{ \left ( - \left ( y \left ( x \right ) \right ) ^{2}+4\,ax-1 \right ) y \left ( x \right ) }}=0} \]
Mathematica: cpu = 0.299038 (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 = 0.656 (sec), leaf count = 308 \[ \left \{ \int _{{\it \_b}}^{x}\!-{\frac { \left ( 4\,{\it \_a}\,a- \left ( y \left ( x \right ) \right ) ^{2} \right ) ^{3}}{64\,{{\it \_a}} ^{3}{a}^{3}-48\,{{\it \_a}}^{2}{a}^{2} \left ( y \left ( x \right ) \right ) ^{2}+12\,{\it \_a}\,a \left ( y \left ( x \right ) \right ) ^{4} - \left ( y \left ( x \right ) \right ) ^{6}-8\,{\it \_a}\,{a}^{2}+2\,a \left ( y \left ( x \right ) \right ) ^{2}+2\,a}}\,{\rm d}{\it \_a}+ \int ^{y \left ( x \right ) }\!{\frac { \left ( -{{\it \_f}}^{2}+4\,ax-1 \right ) {\it \_f}}{-{{\it \_f}}^{6}+12\,{{\it \_f}}^{4}ax-48\,{{\it \_f}}^{2}{a}^{2}{x}^{2}+64\,{a}^{3}{x}^{3}+2\,a{{\it \_f}}^{2}-8\,{a}^ {2}x+2\,a}}-\int _{{\it \_b}}^{x}\!{\frac { \left ( 4\,{\it \_a}\,a-{{ \it \_f}}^{2} \right ) ^{3} \left ( -96\,{{\it \_a}}^{2}{\it \_f}\,{a}^{ 2}+48\,{\it \_a}\,{{\it \_f}}^{3}a-6\,{{\it \_f}}^{5}+4\,a{\it \_f} \right ) }{ \left ( 64\,{{\it \_a}}^{3}{a}^{3}-48\,{{\it \_a}}^{2}{{ \it \_f}}^{2}{a}^{2}+12\,{\it \_a}\,{{\it \_f}}^{4}a-{{\it \_f}}^{6}-8 \,{\it \_a}\,{a}^{2}+2\,a{{\it \_f}}^{2}+2\,a \right ) ^{2}}}+6\,{ \frac { \left ( 4\,{\it \_a}\,a-{{\it \_f}}^{2} \right ) ^{2}{\it \_f}}{ 64\,{{\it \_a}}^{3}{a}^{3}-48\,{{\it \_a}}^{2}{{\it \_f}}^{2}{a}^{2}+ 12\,{\it \_a}\,{{\it \_f}}^{4}a-{{\it \_f}}^{6}-8\,{\it \_a}\,{a}^{2}+ 2\,a{{\it \_f}}^{2}+2\,a}}\,{\rm d}{\it \_a}{d{\it \_f}}+{\it \_C1}=0 \right \} \]