\[ x y(x)^2 y''(x)-a=0 \] ✓ Mathematica : cpu = 0.232431 (sec), leaf count = 116
\[\text {Solve}\left [-\frac {\sqrt {-\frac {2 a y(x)}{x}-\frac {2 c_1 y(x)^2}{x^2}}}{2 c_1}-\frac {a \tan ^{-1}\left (\frac {\sqrt {2} \sqrt {c_1} \left (\frac {y(x)}{x}+\frac {a}{2 c_1}\right )}{\sqrt {-\frac {2 a y(x)}{x}-\frac {2 c_1 y(x)^2}{x^2}}}\right )}{2 \sqrt {2} c_1{}^{3/2}}-\frac {1}{x}-c_2=0,y(x)\right ]\] ✓ Maple : cpu = 9.478 (sec), leaf count = 529
\[ \left \{ y \left ( x \right ) ={\frac {{\it \_C1}\, \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}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 {{\it \_C1}\, \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}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 {{\it \_C1}\, \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}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 {{\it \_C1}\, \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}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 \} \]