\[ x y(x)^2 y''(x)-a=0 \] ✓ Mathematica : cpu = 0.186534 (sec), leaf count = 116
DSolve[-a + x*y[x]^2*Derivative[2][y][x] == 0,y[x],x]
\[\text {Solve}\left [-\frac {a \arctan \left (\frac {\sqrt {2} \sqrt {c_1} \left (\frac {y(x)}{x}+\frac {a}{2 c_1}\right )}{\sqrt {-\frac {2 a y(x)}{x}-\frac {2 c_1 y(x)^2}{x^2}}}\right )}{2 \sqrt {2} c_1{}^{3/2}}-\frac {\sqrt {-\frac {2 a y(x)}{x}-\frac {2 c_1 y(x)^2}{x^2}}}{2 c_1}-\frac {1}{x}-c_2=0,y(x)\right ]\] ✓ Maple : cpu = 1.596 (sec), leaf count = 529
dsolve(x*y(x)^2*diff(diff(y(x),x),x)-a=0,y(x))
\[y \left (x \right ) = \frac {x c_{1} \left (9 c_{1} a +{\mathrm e}^{\operatorname {RootOf}\left (243 \,\operatorname {csgn}\left (\frac {1}{c_{1}}\right ) c_{1}^{4} a^{2} x -54 \textit {\_Z} \,{\mathrm e}^{\textit {\_Z}} a x c_{1}^{3}-3 \,{\mathrm e}^{2 \textit {\_Z}} \operatorname {csgn}\left (\frac {1}{c_{1}}\right ) c_{1}^{2} x -6 \,{\mathrm e}^{\textit {\_Z}} \operatorname {csgn}\left (\frac {1}{c_{1}}\right ) c_{2} x -2 \,{\mathrm e}^{\textit {\_Z}} \operatorname {csgn}\left (\frac {1}{c_{1}}\right )\right )}\right )^{2} {\mathrm e}^{-\operatorname {RootOf}\left (243 \,\operatorname {csgn}\left (\frac {1}{c_{1}}\right ) c_{1}^{4} a^{2} x -54 \textit {\_Z} \,{\mathrm e}^{\textit {\_Z}} a x c_{1}^{3}-3 \,{\mathrm e}^{2 \textit {\_Z}} \operatorname {csgn}\left (\frac {1}{c_{1}}\right ) c_{1}^{2} x -6 \,{\mathrm e}^{\textit {\_Z}} \operatorname {csgn}\left (\frac {1}{c_{1}}\right ) c_{2} x -2 \,{\mathrm e}^{\textit {\_Z}} \operatorname {csgn}\left (\frac {1}{c_{1}}\right )\right )}}{2}\]