\[ y(x)^2 y''(x)-a=0 \] ✓ Mathematica : cpu = 0.165445 (sec), leaf count = 65
DSolve[-a + y[x]^2*Derivative[2][y][x] == 0,y[x],x]
\[\text {Solve}\left [\left (\frac {2 a \text {arctanh}\left (\frac {\sqrt {-\frac {2 a}{y(x)}+c_1}}{\sqrt {c_1}}\right )}{c_1{}^{3/2}}+\frac {y(x) \sqrt {-\frac {2 a}{y(x)}+c_1}}{c_1}\right ){}^2=(x+c_2){}^2,y(x)\right ]\] ✓ Maple : cpu = 0.779 (sec), leaf count = 245
dsolve(y(x)^2*diff(diff(y(x),x),x)-a=0,y(x))
\[y \left (x \right ) = \frac {c_{1} \left (c_{1} a +{\mathrm e}^{\operatorname {RootOf}\left (\operatorname {csgn}\left (\frac {1}{c_{1}}\right ) c_{1}^{4} a^{2}-2 \textit {\_Z} c_{1}^{3} a \,{\mathrm e}^{\textit {\_Z}}-{\mathrm e}^{2 \textit {\_Z}} \operatorname {csgn}\left (\frac {1}{c_{1}}\right ) c_{1}^{2}-2 \,{\mathrm e}^{\textit {\_Z}} \operatorname {csgn}\left (\frac {1}{c_{1}}\right ) c_{2}-2 \,{\mathrm e}^{\textit {\_Z}} \operatorname {csgn}\left (\frac {1}{c_{1}}\right ) x \right )}\right )^{2} {\mathrm e}^{-\operatorname {RootOf}\left (\operatorname {csgn}\left (\frac {1}{c_{1}}\right ) c_{1}^{4} a^{2}-2 \textit {\_Z} c_{1}^{3} a \,{\mathrm e}^{\textit {\_Z}}-{\mathrm e}^{2 \textit {\_Z}} \operatorname {csgn}\left (\frac {1}{c_{1}}\right ) c_{1}^{2}-2 \,{\mathrm e}^{\textit {\_Z}} \operatorname {csgn}\left (\frac {1}{c_{1}}\right ) c_{2}-2 \,{\mathrm e}^{\textit {\_Z}} \operatorname {csgn}\left (\frac {1}{c_{1}}\right ) x \right )}}{2}\]