\[ y'(x)=\frac {\left (4 a x-y(x)^2\right )^3}{y(x) \left (4 a x-y(x)^2-1\right )} \] ✓ Mathematica : cpu = 0.341426 (sec), leaf count = 82
\[\text {Solve}\left [2 a x=\text {RootSum}\left [-\text {$\#$1}^3+2 \text {$\#$1} a-2 a\& ,\frac {\text {$\#$1} a \log \left (-\text {$\#$1}+4 a x-y(x)^2\right )-a \log \left (-\text {$\#$1}+4 a x-y(x)^2\right )}{2 a-3 \text {$\#$1}^2}\& \right ]+c_1,y(x)\right ]\]
✓ Maple : cpu = 37.689 (sec), leaf count = 229
\[ \left \{ \int _{{\it \_b}}^{x}\!-{\frac { \left ( 4\,a{\it \_a}- \left ( y \left ( x \right ) \right ) ^{2} \right ) ^{3}}{- \left ( y \left ( x \right ) \right ) ^{6}+12\,{\it \_a}\,a \left ( y \left ( x \right ) \right ) ^{4}+ \left ( -48\,{{\it \_a}}^{2}{a}^{2}+2\,a \right ) \left ( y \left ( x \right ) \right ) ^{2}+64\,{{\it \_a}}^{3}{a}^{3}-8\,{\it \_a}\,{a}^{2}+2\,a}}\,{\rm d}{\it \_a}+\int ^{y \left ( x \right ) }\!{\frac { \left ( -{{\it \_f}}^{2}+4\,ax-1 \right ) {\it \_f}}{-{{\it \_f}}^{6}+12\,{{\it \_f}}^{4}ax-48\,{{\it \_f}}^{2}{a}^{2}{x}^{2}+64\,{a}^{3}{x}^{3}+2\,{{\it \_f}}^{2}a-8\,{a}^{2}x+2\,a}}-\int _{{\it \_b}}^{x}\!-4\,{\frac { \left ( 4\,a{\it \_a}-{{\it \_f}}^{2} \right ) ^{2}{\it \_f}\,a \left ( 8\,a{\it \_a}-2\,{{\it \_f}}^{2}-3 \right ) }{ \left ( 64\,{{\it \_a}}^{3}{a}^{3}-48\,{{\it \_a}}^{2}{{\it \_f}}^{2}{a}^{2}+12\,{\it \_a}\,{{\it \_f}}^{4}a-{{\it \_f}}^{6}-8\,{\it \_a}\,{a}^{2}+2\,{{\it \_f}}^{2}a+2\,a \right ) ^{2}}}\,{\rm d}{\it \_a}{d{\it \_f}}+{\it \_C1}=0 \right \} \]