2.1692   ODE No. 1692

\[ x^{\frac {n}{n+1}} y''(x)-y(x)^{\frac {2 n+1}{n+1}}=0 \] Mathematica : cpu = 0.0639184 (sec), leaf count = 0


, could not solve

DSolve[-y[x]^((1 + 2*n)/(1 + n)) + x^(n/(1 + n))*Derivative[2][y][x] == 0, y[x], x]

Maple : cpu = 0. (sec), leaf count = 0


, result contains DESol or ODESolStruc

\[y \relax (x ) = \left (\textit {\_a} \,{\mathrm e}^{-\frac {\left (\int \textit {\_}b\left (\textit {\_a} \right )d \textit {\_a} +c_{1}\right ) \left (n +2\right )}{n}}\right )\boldsymbol {\mathrm {where}}\left [\left \{\frac {d}{d \textit {\_a}}\mathrm {\_}\mathrm {b}\left (\textit {\_a} \right )=-\frac {\left (\textit {\_a}^{\frac {2 n +1}{n +1}} n^{2}-2 \textit {\_a} \,n^{2}-6 \textit {\_a} n -4 \textit {\_a} \right ) \textit {\_}b\left (\textit {\_a} \right )^{3}}{n^{2}}-\frac {\left (3 n +4\right ) \textit {\_}b\left (\textit {\_a} \right )^{2}}{n}\right \}, \left \{\textit {\_a} =y \relax (x ) x^{\frac {n +2}{n}}, \textit {\_}b\left (\textit {\_a} \right )=\frac {n \,x^{-\frac {n +2}{n}}}{n x \left (\frac {d}{d x}y \relax (x )\right )+n y \relax (x )+2 y \relax (x )}\right \}, \left \{x ={\mathrm e}^{\int \textit {\_}b\left (\textit {\_a} \right )d \textit {\_a} +c_{1}}, y \relax (x )=\textit {\_a} \,{\mathrm e}^{-\frac {\left (\int \textit {\_}b\left (\textit {\_a} \right )d \textit {\_a} +c_{1}\right ) \left (n +2\right )}{n}}\right \}\right ]\]