2.1660   ODE No. 1660

1. Problem in Latex
2. Mathematica input
3. Maple input

$$y^{″}(x)-x^{n-2}h(x^{-n}y(x),x^{1-n}{y}^{\prime }(x))=0$$ ✗ Mathematica : cpu = 4.43017 (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 = 0.86 (sec), leaf count = 125

$$\{y\left(x\right)=\mathit{O}\mathit{D}\mathit{E}\mathit{S}\mathit{o}\mathit{l}\mathit{S}\mathit{t}\mathit{r}\mathit{u}\mathit{c}(\frac{\mathit{\_}\mathit{a}}{{\mathrm{e}}^{-(\int \mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\mathrm{d}\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1})n}},[\{\frac{\mathrm{d}}{\mathrm{d}\mathit{\_}\mathit{a}}\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)={\left(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)}^2(-\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)h(\mathit{\_}\mathit{a},\frac{\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\mathit{\_}\mathit{a}n+1}{\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)})+n\mathit{\_}\mathit{a}(n-1)\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)+2n-1)\},\{\mathit{\_}\mathit{a}=y\left(x\right)x^{-n},\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)=\frac{1}{x^{-n}(x\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)-ny\left(x\right))}\},\{x={\mathrm{e}}^{\int \mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\mathrm{d}\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1}},y\left(x\right)=\frac{\mathit{\_}\mathit{a}}{{\mathrm{e}}^{-(\int \mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\mathrm{d}\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1})n}}\}])\}$$