2.1663   ODE No. 1663

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

$$-xy(x{)}^n+2y^{\prime }(x)+x{y}^{″}(x)=0$$ ✗ Mathematica : cpu = 0.0232525 (sec), leaf count = 0 , could not solve

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

✓ Maple : cpu = 1.118 (sec), leaf count = 125

$$\{y\left(x\right)=\mathit{O}\mathit{D}\mathit{E}\mathit{S}\mathit{o}\mathit{l}\mathit{S}\mathit{t}\mathit{r}\mathit{u}\mathit{c}(\mathit{\_}\mathit{a}{\mathrm{e}}^{\int \mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\mathrm{d}\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1}},[\{\frac{\mathrm{d}}{\mathrm{d}\mathit{\_}\mathit{a}}\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)=-\frac{(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right){(n-1)}^2{\mathit{\_}\mathit{a}}^n+2\mathit{\_}\mathit{a}(n-3)\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)+2n-10){\left(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)}^2}{4}\},\{\mathit{\_}\mathit{a}=y\left(x\right)x^{2{(n-1)}^{-1}},\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)=-2\frac{1}{(n-1)x\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+2y\left(x\right)}{\left(x^{2{(n-1)}^{-1}}\right)}^{-1}\},\{x={\mathrm{e}}^{-\frac{(\int \mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\mathrm{d}\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1})(n-1)}{2}},y\left(x\right)=\mathit{\_}\mathit{a}{\mathrm{e}}^{\int \mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\mathrm{d}\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1}}\}])\}$$