\[ y(x)^2 y''(x)-a=0 \] ✓ Mathematica : cpu = 0.537859 (sec), leaf count = 75
\[\text {Solve}\left [\left (\frac {y(x) \sqrt {c_1-\frac {2 a}{y(x)}}}{c_1}+\frac {a \log \left (\sqrt {c_1} y(x) \sqrt {c_1-\frac {2 a}{y(x)}}-a+c_1 y(x)\right )}{c_1^{3/2}}\right ){}^2=\left (c_2+x\right ){}^2,y(x)\right ]\]
✓ Maple : cpu = 0.466 (sec), leaf count = 369
\[ \left \{ y \left ( x \right ) ={\frac {{\it \_C1}\, \left ( {{\it \_C1}}^{2}{a}^{2}+2\,{\it \_C1}\,a{{\rm e}^{{\it RootOf} \left ( {\it csgn} \left ( {{\it \_C1}}^{-1} \right ) {{\it \_C1}}^{4}{a}^{2}-2\,{\it \_Z}\,{{\it \_C1}}^{3}a{{\rm e}^{{\it \_Z}}}- \left ( {{\rm e}^{{\it \_Z}}} \right ) ^{2}{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) {{\it \_C1}}^{2}-2\,{{\rm e}^{{\it \_Z}}}{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) {\it \_C2}-2\,{{\rm e}^{{\it \_Z}}}{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) x \right ) }}+ \left ( {{\rm e}^{{\it RootOf} \left ( {\it csgn} \left ( {{\it \_C1}}^{-1} \right ) {{\it \_C1}}^{4}{a}^{2}-2\,{\it \_Z}\,{{\it \_C1}}^{3}a{{\rm e}^{{\it \_Z}}}- \left ( {{\rm e}^{{\it \_Z}}} \right ) ^{2}{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) {{\it \_C1}}^{2}-2\,{{\rm e}^{{\it \_Z}}}{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) {\it \_C2}-2\,{{\rm e}^{{\it \_Z}}}{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) x \right ) }} \right ) ^{2} \right ) }{2\,{{\rm e}^{{\it RootOf} \left ( {\it csgn} \left ( {{\it \_C1}}^{-1} \right ) {{\it \_C1}}^{4}{a}^{2}-2\,{\it \_Z}\,{{\it \_C1}}^{3}a{{\rm e}^{{\it \_Z}}}- \left ( {{\rm e}^{{\it \_Z}}} \right ) ^{2}{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) {{\it \_C1}}^{2}-2\,{{\rm e}^{{\it \_Z}}}{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) {\it \_C2}-2\,{{\rm e}^{{\it \_Z}}}{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) x \right ) }}}},y \left ( x \right ) ={\frac {{\it \_C1}\, \left ( {{\it \_C1}}^{2}{a}^{2}+2\,{\it \_C1}\,a{{\rm e}^{{\it RootOf} \left ( {\it csgn} \left ( {{\it \_C1}}^{-1} \right ) {{\it \_C1}}^{4}{a}^{2}-2\,{\it \_Z}\,{{\it \_C1}}^{3}a{{\rm e}^{{\it \_Z}}}- \left ( {{\rm e}^{{\it \_Z}}} \right ) ^{2}{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) {{\it \_C1}}^{2}+2\,{{\rm e}^{{\it \_Z}}}{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) {\it \_C2}+2\,{{\rm e}^{{\it \_Z}}}{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) x \right ) }}+ \left ( {{\rm e}^{{\it RootOf} \left ( {\it csgn} \left ( {{\it \_C1}}^{-1} \right ) {{\it \_C1}}^{4}{a}^{2}-2\,{\it \_Z}\,{{\it \_C1}}^{3}a{{\rm e}^{{\it \_Z}}}- \left ( {{\rm e}^{{\it \_Z}}} \right ) ^{2}{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) {{\it \_C1}}^{2}+2\,{{\rm e}^{{\it \_Z}}}{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) {\it \_C2}+2\,{{\rm e}^{{\it \_Z}}}{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) x \right ) }} \right ) ^{2} \right ) }{2\,{{\rm e}^{{\it RootOf} \left ( {\it csgn} \left ( {{\it \_C1}}^{-1} \right ) {{\it \_C1}}^{4}{a}^{2}-2\,{\it \_Z}\,{{\it \_C1}}^{3}a{{\rm e}^{{\it \_Z}}}- \left ( {{\rm e}^{{\it \_Z}}} \right ) ^{2}{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) {{\it \_C1}}^{2}+2\,{{\rm e}^{{\it \_Z}}}{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) {\it \_C2}+2\,{{\rm e}^{{\it \_Z}}}{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) x \right ) }}}} \right \} \]