\[ -\frac {2 (n+1) (n+2) y(x) \left (y(x)^{\frac {n}{n+1}}-1\right )}{n^2}-\frac {(3 n+4) y'(x)}{n}+y''(x)=0 \] ✗ Mathematica : cpu = 60.1484 (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 = 4.202 (sec), leaf count = 91
\[\left \{y \left (x \right ) = \mathit {ODESolStruc} \left (\textit {\_a} , \left [\left \{\frac {n^{2} \textit {\_}b\left (\textit {\_a} \right ) \left (\frac {d}{d \textit {\_a}}\mathrm {\_}\mathrm {b}\left (\textit {\_a} \right )\right )-2 \left (n +2\right ) \left (n +1\right ) \textit {\_a} \,\textit {\_a}^{\frac {n}{n +1}}+2 \left (n +1\right ) \left (n +2\right ) \textit {\_a} +\left (-3 n^{2}-4 n \right ) \textit {\_}b\left (\textit {\_a} \right )}{n^{2}}=0\right \}, \left \{\textit {\_a} =y \left (x \right ), \textit {\_}b\left (\textit {\_a} \right )=\frac {d}{d x}y \left (x \right )\right \}, \left \{x =c_{1}+\int \frac {1}{\textit {\_}b\left (\textit {\_a} \right )}d \textit {\_a} , y \left (x \right )=\textit {\_a} \right \}\right ]\right )\right \}\]