\[ y(x)^2 y''(x)-a=0 \] ✓ Mathematica : cpu = 0.266365 (sec), leaf count = 65
\[\text {Solve}\left [\left (\frac {y(x) \sqrt {-\frac {2 a}{y(x)}+c_1}}{c_1}+\frac {2 a \tanh ^{-1}\left (\frac {\sqrt {-\frac {2 a}{y(x)}+c_1}}{\sqrt {c_1}}\right )}{c_1{}^{3/2}}\right ){}^2=(x+c_2){}^2,y(x)\right ]\] ✓ Maple : cpu = 2.039 (sec), leaf count = 245
\[\left \{y \left (x \right ) = \frac {c_{1} \left (c_{1} a +{\mathrm e}^{\RootOf \left (c_{1}^{4} a^{2} \mathrm {csgn}\left (\frac {1}{c_{1}}\right )-2 c_{1}^{3} \textit {\_Z} a \,{\mathrm e}^{\textit {\_Z}}-c_{1}^{2} \mathrm {csgn}\left (\frac {1}{c_{1}}\right ) {\mathrm e}^{2 \textit {\_Z}}-2 c_{2} \mathrm {csgn}\left (\frac {1}{c_{1}}\right ) {\mathrm e}^{\textit {\_Z}}-2 x \,\mathrm {csgn}\left (\frac {1}{c_{1}}\right ) {\mathrm e}^{\textit {\_Z}}\right )}\right )^{2} {\mathrm e}^{-\RootOf \left (c_{1}^{4} a^{2} \mathrm {csgn}\left (\frac {1}{c_{1}}\right )-2 c_{1}^{3} \textit {\_Z} a \,{\mathrm e}^{\textit {\_Z}}-c_{1}^{2} \mathrm {csgn}\left (\frac {1}{c_{1}}\right ) {\mathrm e}^{2 \textit {\_Z}}-2 c_{2} \mathrm {csgn}\left (\frac {1}{c_{1}}\right ) {\mathrm e}^{\textit {\_Z}}-2 x \,\mathrm {csgn}\left (\frac {1}{c_{1}}\right ) {\mathrm e}^{\textit {\_Z}}\right )}}{2}, y \left (x \right ) = \frac {c_{1} \left (c_{1} a +{\mathrm e}^{\RootOf \left (c_{1}^{4} a^{2} \mathrm {csgn}\left (\frac {1}{c_{1}}\right )-2 c_{1}^{3} \textit {\_Z} a \,{\mathrm e}^{\textit {\_Z}}-c_{1}^{2} \mathrm {csgn}\left (\frac {1}{c_{1}}\right ) {\mathrm e}^{2 \textit {\_Z}}+2 c_{2} \mathrm {csgn}\left (\frac {1}{c_{1}}\right ) {\mathrm e}^{\textit {\_Z}}+2 x \,\mathrm {csgn}\left (\frac {1}{c_{1}}\right ) {\mathrm e}^{\textit {\_Z}}\right )}\right )^{2} {\mathrm e}^{-\RootOf \left (c_{1}^{4} a^{2} \mathrm {csgn}\left (\frac {1}{c_{1}}\right )-2 c_{1}^{3} \textit {\_Z} a \,{\mathrm e}^{\textit {\_Z}}-c_{1}^{2} \mathrm {csgn}\left (\frac {1}{c_{1}}\right ) {\mathrm e}^{2 \textit {\_Z}}+2 c_{2} \mathrm {csgn}\left (\frac {1}{c_{1}}\right ) {\mathrm e}^{\textit {\_Z}}+2 x \,\mathrm {csgn}\left (\frac {1}{c_{1}}\right ) {\mathrm e}^{\textit {\_Z}}\right )}}{2}\right \}\]