2.1692   ODE No. 1692

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

$$x^{\frac{n}{n+1}}{y}^{″}(x)-y(x{)}^{\frac{2n+1}{n+1}}=0$$ ✗ Mathematica : cpu = 0.0540371 (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 = 17.604 (sec), leaf count = 156

$$\{y\left(x\right)=\mathit{O}\mathit{D}\mathit{E}\mathit{S}\mathit{o}\mathit{l}\mathit{S}\mathit{t}\mathit{r}\mathit{u}\mathit{c}(\mathit{\_}\mathit{a}{\left({\mathrm{e}}^{\frac{(\int \mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\mathrm{d}\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1})(n+2)}{n}}\right)}^{-1},[\{\frac{\mathrm{d}}{\mathrm{d}\mathit{\_}\mathit{a}}\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)=2\frac{{\left(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)}^2}{n^2}(-1/2{\mathit{\_}\mathit{a}}^{\frac{2n+1}{n+1}}\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)n^2+\mathit{\_}\mathit{a}(n+2)(n+1)\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)-3/2n^2-2n)\},\{\mathit{\_}\mathit{a}=y\left(x\right)x^{\frac{n+2}{n}},\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)=\frac{n}{nx\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+y\left(x\right)(n+2)}{\left(x^{\frac{n+2}{n}}\right)}^{-1}\},\{x={\mathrm{e}}^{\int \mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\mathrm{d}\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1}},y\left(x\right)=\mathit{\_}\mathit{a}{\left({\mathrm{e}}^{\frac{(\int \mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\mathrm{d}\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1})(n+2)}{n}}\right)}^{-1}\}])\}$$