\[ y''(x)-k x^a y(x)^b y'(x)^c=0 \] ✗ Mathematica : cpu = 0.0796613 (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 = 2.064 (sec), leaf count = 413
\[ \left \{ y \left ( x \right ) ={\it ODESolStruc} \left ( {\it \_a}\,{{\rm e}^{\int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+{\it \_C1}}},[ \left \{ {\frac {\rm d}{{\rm d}{\it \_a}}}{\it \_b} \left ( {\it \_a} \right ) =-{\frac { \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{3}}{ \left ( a-c+2 \right ) ^{2}} \left ( {{\it \_a}}^{b} \left ( -{\frac { \left ( a-c+2 \right ) \left ( {\it \_a}\,{\it \_b} \left ( {\it \_a} \right ) +1 \right ) }{{\it \_b} \left ( {\it \_a} \right ) \left ( b+c-1 \right ) }} \right ) ^{c}{b}^{2}k+2\,{{\it \_a}}^{b} \left ( -{\frac { \left ( a-c+2 \right ) \left ( {\it \_a}\,{\it \_b} \left ( {\it \_a} \right ) +1 \right ) }{{\it \_b} \left ( {\it \_a} \right ) \left ( b+c-1 \right ) }} \right ) ^{c}bck+{{\it \_a}}^{b} \left ( -{\frac { \left ( a-c+2 \right ) \left ( {\it \_a}\,{\it \_b} \left ( {\it \_a} \right ) +1 \right ) }{{\it \_b} \left ( {\it \_a} \right ) \left ( b+c-1 \right ) }} \right ) ^{c}{c}^{2}k-2\,{{\it \_a}}^{b} \left ( -{\frac { \left ( a-c+2 \right ) \left ( {\it \_a}\,{\it \_b} \left ( {\it \_a} \right ) +1 \right ) }{{\it \_b} \left ( {\it \_a} \right ) \left ( b+c-1 \right ) }} \right ) ^{c}bk-2\,{{\it \_a}}^{b} \left ( -{\frac { \left ( a-c+2 \right ) \left ( {\it \_a}\,{\it \_b} \left ( {\it \_a} \right ) +1 \right ) }{{\it \_b} \left ( {\it \_a} \right ) \left ( b+c-1 \right ) }} \right ) ^{c}ck+{{\it \_a}}^{b} \left ( -{\frac { \left ( a-c+2 \right ) \left ( {\it \_a}\,{\it \_b} \left ( {\it \_a} \right ) +1 \right ) }{{\it \_b} \left ( {\it \_a} \right ) \left ( b+c-1 \right ) }} \right ) ^{c}k-{\it \_a}\,{a}^{2}-{\it \_a}\,ab+ac{\it \_a}+{\it \_a}\,cb-3\,a{\it \_a}-2\,b{\it \_a}+c{\it \_a}-2\,{\it \_a} \right ) }+{\frac { \left ( 2\,a+b-c+3 \right ) \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{2}}{a-c+2}} \right \} , \left \{ {\it \_a}=y \left ( x \right ) {x}^{{\frac {a-c+2}{b+c-1}}},{\it \_b} \left ( {\it \_a} \right ) =-{\frac {a-c+2}{bx{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +x \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) c+ay \left ( x \right ) -cy \left ( x \right ) -x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +2\,y \left ( x \right ) } \left ( {x}^{{\frac {a-c+2}{b+c-1}}} \right ) ^{-1}} \right \} , \left \{ x={{\rm e}^{-{\frac { \left ( \int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+{\it \_C1} \right ) \left ( b+c-1 \right ) }{a-c+2}}}},y \left ( x \right ) ={\it \_a}\,{{\rm e}^{\int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+{\it \_C1}}} \right \} ] \right ) \right \} \]