\[ x y(x)^2 y''(x)-a=0 \] ✓ Mathematica : cpu = 0.341001 (sec), leaf count = 103
\[\text {Solve}\left [2 \sqrt {2} \sqrt {-\frac {y(x) \left (a x+c_1 y(x)\right )}{x^2}}+\frac {\sqrt {2} a \tan ^{-1}\left (\frac {a x+2 c_1 y(x)}{2 \sqrt {c_1} x \sqrt {-\frac {y(x) \left (a x+c_1 y(x)\right )}{x^2}}}\right )}{\sqrt {c_1}}+\frac {4 c_1}{x}+4 c_1 c_2=0,y(x)\right ]\]
✓ Maple : cpu = 1.237 (sec), leaf count = 529
\[ \left \{ y \left ( x \right ) ={\frac { \left ( 9\,{\it \_C1}\,a+{{\rm e}^{{\it RootOf} \left ( 243\,{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) {{\it \_C1}}^{4}{a}^{2}x-54\,{\it \_Z}\,{{\rm e}^{{\it \_Z}}}ax{{\it \_C1}}^{3}-3\, \left ( {{\rm e}^{{\it \_Z}}} \right ) ^{2}{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) {{\it \_C1}}^{2}x-6\,{{\rm e}^{{\it \_Z}}}{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) {\it \_C2}\,x-2\,{{\rm e}^{{\it \_Z}}}{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) \right ) }} \right ) ^{2}{\it \_C1}\,x}{2\,{{\rm e}^{{\it RootOf} \left ( 243\,{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) {{\it \_C1}}^{4}{a}^{2}x-54\,{\it \_Z}\,{{\rm e}^{{\it \_Z}}}ax{{\it \_C1}}^{3}-3\, \left ( {{\rm e}^{{\it \_Z}}} \right ) ^{2}{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) {{\it \_C1}}^{2}x-6\,{{\rm e}^{{\it \_Z}}}{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) {\it \_C2}\,x-2\,{{\rm e}^{{\it \_Z}}}{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) \right ) }}}},y \left ( x \right ) ={\frac { \left ( 9\,{\it \_C1}\,a+{{\rm e}^{{\it RootOf} \left ( 243\,{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) {{\it \_C1}}^{4}{a}^{2}x-54\,{\it \_Z}\,{{\rm e}^{{\it \_Z}}}ax{{\it \_C1}}^{3}-3\, \left ( {{\rm e}^{{\it \_Z}}} \right ) ^{2}{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) {{\it \_C1}}^{2}x+6\,{{\rm e}^{{\it \_Z}}}{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) {\it \_C2}\,x+2\,{{\rm e}^{{\it \_Z}}}{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) \right ) }} \right ) ^{2}{\it \_C1}\,x}{2\,{{\rm e}^{{\it RootOf} \left ( 243\,{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) {{\it \_C1}}^{4}{a}^{2}x-54\,{\it \_Z}\,{{\rm e}^{{\it \_Z}}}ax{{\it \_C1}}^{3}-3\, \left ( {{\rm e}^{{\it \_Z}}} \right ) ^{2}{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) {{\it \_C1}}^{2}x+6\,{{\rm e}^{{\it \_Z}}}{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) {\it \_C2}\,x+2\,{{\rm e}^{{\it \_Z}}}{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) \right ) }}}},y \left ( x \right ) ={\frac { \left ( 9\,{\it \_C1}\,a+{{\rm e}^{{\it RootOf} \left ( 243\,{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) {{\it \_C1}}^{4}{a}^{2}x+54\,{\it \_Z}\,{{\rm e}^{{\it \_Z}}}ax{{\it \_C1}}^{3}-3\, \left ( {{\rm e}^{{\it \_Z}}} \right ) ^{2}{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) {{\it \_C1}}^{2}x-6\,{{\rm e}^{{\it \_Z}}}{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) {\it \_C2}\,x-2\,{{\rm e}^{{\it \_Z}}}{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) \right ) }} \right ) ^{2}{\it \_C1}\,x}{2\,{{\rm e}^{{\it RootOf} \left ( 243\,{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) {{\it \_C1}}^{4}{a}^{2}x+54\,{\it \_Z}\,{{\rm e}^{{\it \_Z}}}ax{{\it \_C1}}^{3}-3\, \left ( {{\rm e}^{{\it \_Z}}} \right ) ^{2}{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) {{\it \_C1}}^{2}x-6\,{{\rm e}^{{\it \_Z}}}{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) {\it \_C2}\,x-2\,{{\rm e}^{{\it \_Z}}}{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) \right ) }}}},y \left ( x \right ) ={\frac { \left ( 9\,{\it \_C1}\,a+{{\rm e}^{{\it RootOf} \left ( 243\,{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) {{\it \_C1}}^{4}{a}^{2}x+54\,{\it \_Z}\,{{\rm e}^{{\it \_Z}}}ax{{\it \_C1}}^{3}-3\, \left ( {{\rm e}^{{\it \_Z}}} \right ) ^{2}{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) {{\it \_C1}}^{2}x+6\,{{\rm e}^{{\it \_Z}}}{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) {\it \_C2}\,x+2\,{{\rm e}^{{\it \_Z}}}{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) \right ) }} \right ) ^{2}{\it \_C1}\,x}{2\,{{\rm e}^{{\it RootOf} \left ( 243\,{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) {{\it \_C1}}^{4}{a}^{2}x+54\,{\it \_Z}\,{{\rm e}^{{\it \_Z}}}ax{{\it \_C1}}^{3}-3\, \left ( {{\rm e}^{{\it \_Z}}} \right ) ^{2}{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) {{\it \_C1}}^{2}x+6\,{{\rm e}^{{\it \_Z}}}{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) {\it \_C2}\,x+2\,{{\rm e}^{{\it \_Z}}}{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) \right ) }}}} \right \} \]