\[ x y(x)^2 y''(x)-a=0 \] ✓ Mathematica : cpu = 0.330618 (sec), leaf count = 116
\[\text {Solve}\left [-\frac {\sqrt {-\frac {2 a y(x)}{x}-\frac {2 c_1 y(x)^2}{x^2}}}{2 c_1}-\frac {a \tan ^{-1}\left (\frac {\sqrt {2} \sqrt {c_1} \left (\frac {a}{2 c_1}+\frac {y(x)}{x}\right )}{\sqrt {-\frac {2 a y(x)}{x}-\frac {2 c_1 y(x)^2}{x^2}}}\right )}{2 \sqrt {2} c_1^{3/2}}-c_2-\frac {1}{x}=0,y(x)\right ]\] ✓ Maple : cpu = 1.332 (sec), leaf count = 529
\[ \left \{ y \left ( x \right ) ={\frac { \left ( 9\,a{\it \_C1}+{{\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\,{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) \left ( {{\rm e}^{{\it \_Z}}} \right ) ^{2}{{\it \_C1}}^{2}x-6\,{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) {{\rm e}^{{\it \_Z}}}{\it \_C2}\,x-2\,{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) {{\rm e}^{{\it \_Z}}} \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\,{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) \left ( {{\rm e}^{{\it \_Z}}} \right ) ^{2}{{\it \_C1}}^{2}x-6\,{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) {{\rm e}^{{\it \_Z}}}{\it \_C2}\,x-2\,{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) {{\rm e}^{{\it \_Z}}} \right ) }}}},y \left ( x \right ) ={\frac { \left ( 9\,a{\it \_C1}+{{\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\,{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) \left ( {{\rm e}^{{\it \_Z}}} \right ) ^{2}{{\it \_C1}}^{2}x+6\,{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) {{\rm e}^{{\it \_Z}}}{\it \_C2}\,x+2\,{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) {{\rm e}^{{\it \_Z}}} \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\,{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) \left ( {{\rm e}^{{\it \_Z}}} \right ) ^{2}{{\it \_C1}}^{2}x+6\,{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) {{\rm e}^{{\it \_Z}}}{\it \_C2}\,x+2\,{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) {{\rm e}^{{\it \_Z}}} \right ) }}}},y \left ( x \right ) ={\frac { \left ( 9\,a{\it \_C1}+{{\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\,{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) \left ( {{\rm e}^{{\it \_Z}}} \right ) ^{2}{{\it \_C1}}^{2}x-6\,{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) {{\rm e}^{{\it \_Z}}}{\it \_C2}\,x-2\,{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) {{\rm e}^{{\it \_Z}}} \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\,{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) \left ( {{\rm e}^{{\it \_Z}}} \right ) ^{2}{{\it \_C1}}^{2}x-6\,{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) {{\rm e}^{{\it \_Z}}}{\it \_C2}\,x-2\,{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) {{\rm e}^{{\it \_Z}}} \right ) }}}},y \left ( x \right ) ={\frac { \left ( 9\,a{\it \_C1}+{{\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\,{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) \left ( {{\rm e}^{{\it \_Z}}} \right ) ^{2}{{\it \_C1}}^{2}x+6\,{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) {{\rm e}^{{\it \_Z}}}{\it \_C2}\,x+2\,{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) {{\rm e}^{{\it \_Z}}} \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\,{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) \left ( {{\rm e}^{{\it \_Z}}} \right ) ^{2}{{\it \_C1}}^{2}x+6\,{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) {{\rm e}^{{\it \_Z}}}{\it \_C2}\,x+2\,{\it csgn} \left ( {{\it \_C1}}^{-1} \right ) {{\rm e}^{{\it \_Z}}} \right ) }}}} \right \} \]