\[ \boxed { x \left ( y \left ( x \right ) \right ) ^{2}{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) -a=0} \]
Mathematica: cpu = 0.259533 (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 = 2.262 (sec), leaf count = 793 \[ \left \{ y \left ( x \right ) ={\frac {{\it \_C1}\,x \left ( 81\,{{\it \_C1}}^{2}{a}^{2}+18\,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 ) }}+ \left ( { {\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} \right ) }{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 {{\it \_C1}\,x \left ( 81\,{{\it \_C1}}^{2}{a}^{2}+18 \,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 ) }}+ \left ( {{\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} \right ) }{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 {{\it \_C1}\,x \left ( 81\,{{\it \_C1}}^{2}{a}^{2}+18\,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 ) }}+ \left ( {{\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} \right ) }{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 {{\it \_C1}\,x \left ( 81\,{ {\it \_C1}}^{2}{a}^{2}+18\,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 ) }}+ \left ( { {\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} \right ) }{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 \} \]