8.74   ODE No. 1664

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

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

Mathematica: cpu = 0.537568 (sec), leaf count = 28 $$\text{DSolve}[a{x}^{m}y(x{)}^n+x{y}^{″}(x)+2y^{\prime }(x)=0,y(x),x]$$

Maple: cpu = 2.355 (sec), leaf count = 185 $$\{y\left(x\right)=\mathit{O}\mathit{D}\mathit{E}\mathit{S}\mathit{o}\mathit{l}\mathit{S}\mathit{t}\mathit{r}\mathit{u}\mathit{c}(\mathit{\_}\mathit{a}{\mathrm{e}}^{\int \mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\mathrm{d}\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1}},[\{\frac{\mathrm{d}}{\mathrm{d}\mathit{\_}\mathit{a}}\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)=\frac{({\mathit{\_}\mathit{a}}^{n}a{n}^2-2{\mathit{\_}\mathit{a}}^{n}an+\mathit{\_}\mathit{a}{m}^2-\mathit{\_}\mathit{a}mn+{\mathit{\_}\mathit{a}}^{n}a+3\mathit{\_}\mathit{a}m-\mathit{\_}\mathit{a}n+2\mathit{\_}\mathit{a}){\left(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)}^3}{{(m+1)}^2}+\frac{(2m-n+3){\left(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)}^2}{m+1}\},\{\mathit{\_}\mathit{a}=y\left(x\right)x^{\frac{m+1}{n-1}},\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)=-\frac{m+1}{nx\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+y\left(x\right)m-x\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+y\left(x\right)}{\left(x^{\frac{m+1}{n-1}}\right)}^{-1}\},\{x={\mathrm{e}}^{-\frac{(\int \mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\mathrm{d}\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1})(n-1)}{m+1}},y\left(x\right)=\mathit{\_}\mathit{a}{\mathrm{e}}^{\int \mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\mathrm{d}\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1}}\}])\}$$