\[ y''(x)-x^{n-2} h\left (x^{-n} y(x),x^{1-n} y'(x)\right )=0 \] ✗ Mathematica : cpu = 2.48613 (sec), leaf count = 0
DSolve[-(x^(-2 + n)*h[y[x]/x^n, x^(1 - n)*Derivative[1][y][x]]) + Derivative[2][y][x] == 0,y[x],x]
, 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
dsolve(diff(diff(y(x),x),x)-x^(n-2)*h(y(x)/(x^n),diff(y(x),x)/(x^(n-1)))=0,y(x))
, result contains DESol or ODESolStruc
\[y \left (x \right ) = \left (\textit {\_a} \,{\mathrm e}^{\left (\int \textit {\_}b\left (\textit {\_a} \right )d \textit {\_a} +c_{1}\right ) n}\right )\boldsymbol {\mathrm {where}}\left [\left \{\frac {d}{d \textit {\_a}}\mathrm {\_}\mathrm {b}\left (\textit {\_a} \right )=\left (\textit {\_a} \,n^{2}-\textit {\_a} n -h \left (\textit {\_a} , \frac {\textit {\_}b\left (\textit {\_a} \right ) \textit {\_a} n +1}{\textit {\_}b\left (\textit {\_a} \right )}\right )\right ) \textit {\_}b\left (\textit {\_a} \right )^{3}+\left (2 n -1\right ) \textit {\_}b\left (\textit {\_a} \right )^{2}\right \}, \left \{\textit {\_a} =y \left (x \right ) x^{-n}, \textit {\_}b\left (\textit {\_a} \right )=\frac {x^{n}}{x \left (\frac {d}{d x}y \left (x \right )\right )-n y \left (x \right )}\right \}, \left \{x ={\mathrm e}^{\int \textit {\_}b\left (\textit {\_a} \right )d \textit {\_a} +c_{1}}, y \left (x \right )=\textit {\_a} \,{\mathrm e}^{\left (\int \textit {\_}b\left (\textit {\_a} \right )d \textit {\_a} +c_{1}\right ) n}\right \}\right ]\]