\[ a x^m y(x)^n+2 y'(x)+x y''(x)=0 \] ✗ Mathematica : cpu = 0.16551 (sec), leaf count = 0 , could not solve
DSolve[a*x^m*y[x]^n + 2*Derivative[1][y][x] + x*Derivative[2][y][x] == 0, y[x], x]
✓ Maple : cpu = 4.555 (sec), leaf count = 155
\[ \left \{ y \left ( x \right ) ={\it ODESolStruc} \left ( {\it \_a}\,{{\rm e}^{\int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+{\it \_C1}}},[ \left \{ {\frac {\rm d}{{\rm d}{\it \_a}}}{\it \_b} \left ( {\it \_a} \right ) ={\frac { \left ( a{\it \_b} \left ( {\it \_a} \right ) \left ( n-1 \right ) ^{2}{{\it \_a}}^{n}+ \left ( {\it \_a}\, \left ( m-n+2 \right ) {\it \_b} \left ( {\it \_a} \right ) +2\,m+3-n \right ) \left ( m+1 \right ) \right ) \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{2}}{ \left ( m+1 \right ) ^{2}}} \right \} , \left \{ {\it \_a}=y \left ( x \right ) {x}^{{\frac {m+1}{n-1}}},{\it \_b} \left ( {\it \_a} \right ) ={\frac {-m-1}{ \left ( n-1 \right ) x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +y \left ( x \right ) \left ( m+1 \right ) } \left ( {x}^{{\frac {m+1}{n-1}}} \right ) ^{-1}} \right \} , \left \{ x={{\rm e}^{-{\frac { \left ( \int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+{\it \_C1} \right ) \left ( n-1 \right ) }{m+1}}}},y \left ( x \right ) ={\it \_a}\,{{\rm e}^{\int \!{\it \_b} \left ( {\it \_a} \right ) \,{\rm d}{\it \_a}+{\it \_C1}}} \right \} ] \right ) \right \} \]