\[ \boxed { \left ( y \left ( x \right ) \right ) ^{2}{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) -a=0} \]
Mathematica: cpu = 0.537568 (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 = 1.950 (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}}}-{\it csgn} \left ( {{\it \_C1} }^{-1} \right ) \left ( {{\rm e}^{{\it \_Z}}} \right ) ^{2}{{\it \_C1}}^ {2}-2\,{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) {{\rm e}^{{\it \_Z} }}{\it \_C2}-2\,{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) {{\rm e}^{ {\it \_Z}}}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}}}-{\it csgn} \left ( {{ \it \_C1}}^{-1} \right ) \left ( {{\rm e}^{{\it \_Z}}} \right ) ^{2}{{ \it \_C1}}^{2}-2\,{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) {{\rm e} ^{{\it \_Z}}}{\it \_C2}-2\,{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) {{\rm e}^{{\it \_Z}}}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}}}-{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) \left ( {{\rm e}^{{\it \_Z}}} \right ) ^{2}{{\it \_C1}}^{2}-2\,{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) {{\rm e}^{{\it \_Z}}}{\it \_C2} -2\,{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) {{\rm e}^{{\it \_Z}}}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}}}-{\it csgn} \left ( {{ \it \_C1}}^{-1} \right ) \left ( {{\rm e}^{{\it \_Z}}} \right ) ^{2}{{ \it \_C1}}^{2}+2\,{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) {{\rm e} ^{{\it \_Z}}}{\it \_C2}+2\,{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) {{\rm e}^{{\it \_Z}}}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}}}-{ \it csgn} \left ( {{\it \_C1}}^{-1} \right ) \left ( {{\rm e}^{{\it \_Z} }} \right ) ^{2}{{\it \_C1}}^{2}+2\,{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) {{\rm e}^{{\it \_Z}}}{\it \_C2}+2\,{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) {{\rm e}^{{\it \_Z}}}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}}}-{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) \left ( {{\rm e}^{{\it \_Z}}} \right ) ^{2}{{\it \_C1}}^{2}+2 \,{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) {{\rm e}^{{\it \_Z}}}{ \it \_C2}+2\,{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) {{\rm e}^{{ \it \_Z}}}x \right ) }}}} \right \} \]