8.73   ODE No. 1663

$$\boxed{{\displaystyle x\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)+2\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)-x{\left(y\left(x\right)\right)}^n=0}}$$

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

Mathematica: cpu = 0.037005 (sec), leaf count = 26 $$\text{DSolve}[-xy(x{)}^n+x{y}^{″}(x)+2y^{\prime }(x)=0,y(x),x]$$

Maple: cpu = 0.593 (sec), leaf count = 151 $$\{y\left(x\right)=\mathit{O}\mathit{D}\mathit{E}\mathit{S}\mathit{o}\mathit{l}\mathit{S}\mathit{t}\mathit{r}\mathit{u}\mathit{c}(\mathit{\_}\mathit{a}{\mathrm{e}}^{\int \mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\mathrm{d}\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1}},[\{\frac{\mathrm{d}}{\mathrm{d}\mathit{\_}\mathit{a}}\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)=(-\frac{{\mathit{\_}\mathit{a}}^n{n}^2}{4}+\frac{{\mathit{\_}\mathit{a}}^{n}n}{2}-\frac{\mathit{\_}\mathit{a}n}{2}-\frac{{\mathit{\_}\mathit{a}}^n}{4}+\frac{3\mathit{\_}\mathit{a}}{2}){\left(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)}^3+(-\frac{n}{2}+\frac{5}{2}){\left(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)}^2\},\{\mathit{\_}\mathit{a}=y\left(x\right)x^{2{(n-1)}^{-1}},\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)=-2\frac{1}{nx\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)-x\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+2y\left(x\right)}{\left(x^{2{(n-1)}^{-1}}\right)}^{-1}\},\{x={\mathrm{e}}^{-\frac{(\int \mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\mathrm{d}\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1})n}{2}+\frac{\int \mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\mathrm{d}\mathit{\_}\mathit{a}}{2}+\frac{\mathit{\_}\mathit{C}\mathit{1}}{2}},y\left(x\right)=\mathit{\_}\mathit{a}{\mathrm{e}}^{\int \mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\mathrm{d}\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1}}\}])\}$$