2.1660   ODE No. 1660

\[ y''(x)-x^{n-2} h\left (x^{-n} y(x),x^{1-n} y'(x)\right )=0 \] Mathematica : cpu = 2.48613 (sec), leaf count = 0


, could not solve

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

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


, result contains DESol or ODESolStruc

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