8.26   ODE No. 1616

$$\boxed{{\displaystyle \frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)+a\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+b{\left(y\left(x\right)\right)}^n+1/4(a^2-1)y\left(x\right)=0}}$$

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

Mathematica: cpu = 25.262208 (sec), leaf count = 34 $$\text{DSolve}[\frac{1}{4}(a^2-1)y(x)+a{y}^{\prime }(x)+by(x{)}^n+y^{″}(x)=0,y(x),x]$$

Maple: cpu = 0.889 (sec), leaf count = 63 $$\{y\left(x\right)=\mathit{O}\mathit{D}\mathit{E}\mathit{S}\mathit{o}\mathit{l}\mathit{S}\mathit{t}\mathit{r}\mathit{u}\mathit{c}(\mathit{\_}\mathit{a},[\{\left(\frac{\mathrm{d}}{\mathrm{d}\mathit{\_}\mathit{a}}\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)+a\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)+b{\mathit{\_}\mathit{a}}^n+\frac{\mathit{\_}\mathit{a}{a}^2}{4}-\frac{\mathit{\_}\mathit{a}}{4}=0\},\{\mathit{\_}\mathit{a}=y\left(x\right),\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)=\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\},\{x=\int {\left(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)}^{-1}\mathrm{d}\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1},y\left(x\right)=\mathit{\_}\mathit{a}\}])\}$$