\[ -\frac {2 (n+1) (n+2) y(x) \left (y(x)^{\frac {n}{n+1}}-1\right )}{n^2}-\frac {(3 n+4) y'(x)}{n}+y''(x)=0 \] ✗ Mathematica : cpu = 75.3693 (sec), leaf count = 0 , could not solve
DSolve[(-2*(1 + n)*(2 + n)*y[x]*(-1 + y[x]^(n/(1 + n))))/n^2 - ((4 + 3*n)*Derivative[1][y][x])/n + Derivative[2][y][x] == 0, y[x], x]
✓ Maple : cpu = 12.922 (sec), leaf count = 91
\[ \left \{ y \left ( x \right ) ={\it ODESolStruc} \left ( {\it \_a},[ \left \{ {\frac {1}{{n}^{2}} \left ( -2\, \left ( n+2 \right ) \left ( n+1 \right ) {\it \_a}\,{{\it \_a}}^{{\frac {n}{n+1}}}+ \left ( {\frac {\rm d}{{\rm d}{\it \_a}}}{\it \_b} \left ( {\it \_a} \right ) \right ) {\it \_b} \left ( {\it \_a} \right ) {n}^{2}+ \left ( -3\,{n}^{2}-4\,n \right ) {\it \_b} \left ( {\it \_a} \right ) +2\, \left ( n+2 \right ) \left ( n+1 \right ) {\it \_a} \right ) }=0 \right \} , \left \{ {\it \_a}=y \left ( x \right ) ,{\it \_b} \left ( {\it \_a} \right ) ={\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right \} , \left \{ x=\int \! \left ( {\it \_b} \left ( {\it \_a} \right ) \right ) ^{-1}\,{\rm d}{\it \_a}+{\it \_C1},y \left ( x \right ) ={\it \_a} \right \} ] \right ) \right \} \]