\[ y''(x)-k x^a y(x)^b y'(x)^c=0 \] ✗ Mathematica : cpu = 0.0735638 (sec), leaf count = 0 , could not solve
DSolve[-(k*x^a*y[x]^b*Derivative[1][y][x]^c) + Derivative[2][y][x] == 0, y[x], x]
✓ Maple : cpu = 1.552 (sec), leaf count = 205
\[\left \{y \left (x \right ) = \mathit {ODESolStruc} \left (\textit {\_a} \,{\mathrm e}^{c_{1}+\int \textit {\_}b\left (\textit {\_a} \right )d \textit {\_a}}, \left [\left \{\frac {d}{d \textit {\_a}}\mathrm {\_}\mathrm {b}\left (\textit {\_a} \right )=\frac {\left (-\left (b +c -1\right )^{2} k \,\textit {\_a}^{b} \left (-\frac {\left (a -c +2\right ) \left (\textit {\_a} \textit {\_}b\left (\textit {\_a} \right )+1\right )}{\left (b +c -1\right ) \textit {\_}b\left (\textit {\_a} \right )}\right )^{c} \textit {\_}b\left (\textit {\_a} \right )+\left (a -c +2\right ) \left (\left (a +b +1\right ) \textit {\_a} \textit {\_}b\left (\textit {\_a} \right )+2 a +b -c +3\right )\right ) \textit {\_}b\left (\textit {\_a} \right )^{2}}{\left (a -c +2\right )^{2}}\right \}, \left \{\textit {\_a} =x^{\frac {a -c +2}{b +c -1}} y \left (x \right ), \textit {\_}b\left (\textit {\_a} \right )=\frac {\left (-a +c -2\right ) x^{-\frac {a -c +2}{b +c -1}}}{\left (b +c -1\right ) x \left (\frac {d}{d x}y \left (x \right )\right )+\left (a -c +2\right ) y \left (x \right )}\right \}, \left \{x ={\mathrm e}^{-\frac {\left (c_{1}+\int \textit {\_}b\left (\textit {\_a} \right )d \textit {\_a} \right ) \left (b +c -1\right )}{a -c +2}}, y \left (x \right )=\textit {\_a} \,{\mathrm e}^{c_{1}+\int \textit {\_}b\left (\textit {\_a} \right )d \textit {\_a}}\right \}\right ]\right )\right \}\]