\[ x y(x)^2 y''(x)-a=0 \] ✓ Mathematica : cpu = 0.351018 (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 = 3.092 (sec), leaf count = 529
\[\left \{y \left (x \right ) = \frac {c_{1} \left (9 c_{1} a +{\mathrm e}^{\RootOf \left (243 c_{1}^{4} a^{2} x \,\mathrm {csgn}\left (\frac {1}{c_{1}}\right )-54 c_{1}^{3} \textit {\_Z} a x \,{\mathrm e}^{\textit {\_Z}}-3 c_{1}^{2} x \,\mathrm {csgn}\left (\frac {1}{c_{1}}\right ) {\mathrm e}^{2 \textit {\_Z}}-6 c_{2} x \,\mathrm {csgn}\left (\frac {1}{c_{1}}\right ) {\mathrm e}^{\textit {\_Z}}-2 \,\mathrm {csgn}\left (\frac {1}{c_{1}}\right ) {\mathrm e}^{\textit {\_Z}}\right )}\right )^{2} x \,{\mathrm e}^{-\RootOf \left (243 c_{1}^{4} a^{2} x \,\mathrm {csgn}\left (\frac {1}{c_{1}}\right )-54 c_{1}^{3} \textit {\_Z} a x \,{\mathrm e}^{\textit {\_Z}}-3 c_{1}^{2} x \,\mathrm {csgn}\left (\frac {1}{c_{1}}\right ) {\mathrm e}^{2 \textit {\_Z}}-6 c_{2} x \,\mathrm {csgn}\left (\frac {1}{c_{1}}\right ) {\mathrm e}^{\textit {\_Z}}-2 \,\mathrm {csgn}\left (\frac {1}{c_{1}}\right ) {\mathrm e}^{\textit {\_Z}}\right )}}{2}, y \left (x \right ) = \frac {c_{1} \left (9 c_{1} a +{\mathrm e}^{\RootOf \left (243 c_{1}^{4} a^{2} x \,\mathrm {csgn}\left (\frac {1}{c_{1}}\right )-54 c_{1}^{3} \textit {\_Z} a x \,{\mathrm e}^{\textit {\_Z}}-3 c_{1}^{2} x \,\mathrm {csgn}\left (\frac {1}{c_{1}}\right ) {\mathrm e}^{2 \textit {\_Z}}+6 c_{2} x \,\mathrm {csgn}\left (\frac {1}{c_{1}}\right ) {\mathrm e}^{\textit {\_Z}}+2 \,\mathrm {csgn}\left (\frac {1}{c_{1}}\right ) {\mathrm e}^{\textit {\_Z}}\right )}\right )^{2} x \,{\mathrm e}^{-\RootOf \left (243 c_{1}^{4} a^{2} x \,\mathrm {csgn}\left (\frac {1}{c_{1}}\right )-54 c_{1}^{3} \textit {\_Z} a x \,{\mathrm e}^{\textit {\_Z}}-3 c_{1}^{2} x \,\mathrm {csgn}\left (\frac {1}{c_{1}}\right ) {\mathrm e}^{2 \textit {\_Z}}+6 c_{2} x \,\mathrm {csgn}\left (\frac {1}{c_{1}}\right ) {\mathrm e}^{\textit {\_Z}}+2 \,\mathrm {csgn}\left (\frac {1}{c_{1}}\right ) {\mathrm e}^{\textit {\_Z}}\right )}}{2}, y \left (x \right ) = \frac {c_{1} \left (9 c_{1} a +{\mathrm e}^{\RootOf \left (243 c_{1}^{4} a^{2} x \,\mathrm {csgn}\left (\frac {1}{c_{1}}\right )+54 c_{1}^{3} \textit {\_Z} a x \,{\mathrm e}^{\textit {\_Z}}-3 c_{1}^{2} x \,\mathrm {csgn}\left (\frac {1}{c_{1}}\right ) {\mathrm e}^{2 \textit {\_Z}}-6 c_{2} x \,\mathrm {csgn}\left (\frac {1}{c_{1}}\right ) {\mathrm e}^{\textit {\_Z}}-2 \,\mathrm {csgn}\left (\frac {1}{c_{1}}\right ) {\mathrm e}^{\textit {\_Z}}\right )}\right )^{2} x \,{\mathrm e}^{-\RootOf \left (243 c_{1}^{4} a^{2} x \,\mathrm {csgn}\left (\frac {1}{c_{1}}\right )+54 c_{1}^{3} \textit {\_Z} a x \,{\mathrm e}^{\textit {\_Z}}-3 c_{1}^{2} x \,\mathrm {csgn}\left (\frac {1}{c_{1}}\right ) {\mathrm e}^{2 \textit {\_Z}}-6 c_{2} x \,\mathrm {csgn}\left (\frac {1}{c_{1}}\right ) {\mathrm e}^{\textit {\_Z}}-2 \,\mathrm {csgn}\left (\frac {1}{c_{1}}\right ) {\mathrm e}^{\textit {\_Z}}\right )}}{2}, y \left (x \right ) = \frac {c_{1} \left (9 c_{1} a +{\mathrm e}^{\RootOf \left (243 c_{1}^{4} a^{2} x \,\mathrm {csgn}\left (\frac {1}{c_{1}}\right )+54 c_{1}^{3} \textit {\_Z} a x \,{\mathrm e}^{\textit {\_Z}}-3 c_{1}^{2} x \,\mathrm {csgn}\left (\frac {1}{c_{1}}\right ) {\mathrm e}^{2 \textit {\_Z}}+6 c_{2} x \,\mathrm {csgn}\left (\frac {1}{c_{1}}\right ) {\mathrm e}^{\textit {\_Z}}+2 \,\mathrm {csgn}\left (\frac {1}{c_{1}}\right ) {\mathrm e}^{\textit {\_Z}}\right )}\right )^{2} x \,{\mathrm e}^{-\RootOf \left (243 c_{1}^{4} a^{2} x \,\mathrm {csgn}\left (\frac {1}{c_{1}}\right )+54 c_{1}^{3} \textit {\_Z} a x \,{\mathrm e}^{\textit {\_Z}}-3 c_{1}^{2} x \,\mathrm {csgn}\left (\frac {1}{c_{1}}\right ) {\mathrm e}^{2 \textit {\_Z}}+6 c_{2} x \,\mathrm {csgn}\left (\frac {1}{c_{1}}\right ) {\mathrm e}^{\textit {\_Z}}+2 \,\mathrm {csgn}\left (\frac {1}{c_{1}}\right ) {\mathrm e}^{\textit {\_Z}}\right )}}{2}\right \}\]