\[ -\frac {2 (n+1) (n+2) y(x) \left (y(x)^{\frac {n}{n+1}}-1\right )}{n^2}-\frac {(3 n+4) y'(x)}{n}+y''(x)=0 \] ✗ Mathematica : cpu = 60.1188 (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 = 0. (sec), leaf count = 0
, result contains DESol or ODESolStruc
\[y \relax (x ) = \textit {\_a} \boldsymbol {\mathrm {where}}\left [\left \{\left (\frac {d}{d \textit {\_a}}\mathrm {\_}\mathrm {b}\left (\textit {\_a} \right )\right ) \textit {\_}b\left (\textit {\_a} \right )-\frac {2 \textit {\_a}^{\frac {n}{n +1}} \textit {\_a} \,n^{2}+6 \textit {\_a}^{\frac {n}{n +1}} \textit {\_a} n +3 \textit {\_}b\left (\textit {\_a} \right ) n^{2}-2 \textit {\_a} \,n^{2}+4 \textit {\_a}^{\frac {n}{n +1}} \textit {\_a} +4 \textit {\_}b\left (\textit {\_a} \right ) n -6 \textit {\_a} n -4 \textit {\_a}}{n^{2}}=0\right \}, \left \{\textit {\_a} =y \relax (x ), \textit {\_}b\left (\textit {\_a} \right )=\frac {d}{d x}y \relax (x )\right \}, \left \{x =\int \frac {1}{\textit {\_}b\left (\textit {\_a} \right )}d \textit {\_a} +c_{1}, y \relax (x )=\textit {\_a} \right \}\right ]\]