8.25   ODE No. 1615

$$\boxed{{\displaystyle \frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)-\frac{(3n+4)\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)}{n}-2\frac{(n+1)(n+2)y\left(x\right)}{n^2}({\left(y\left(x\right)\right)}^{\frac{n}{n+1}}-1)=0}}$$

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

Mathematica: cpu = 118.097997 (sec), leaf count = 50 $$\text{DSolve}[-\frac{2(n+1)(n+2)y(x)(y(x{)}^{\frac{n}{n+1}}-1)}{n^2}-\frac{(3n+4)y^{\prime }(x)}{n}+y^{″}(x)=0,y(x),x]$$

Maple: cpu = 3.526 (sec), leaf count = 116 $$\{y\left(x\right)=\mathit{O}\mathit{D}\mathit{E}\mathit{S}\mathit{o}\mathit{l}\mathit{S}\mathit{t}\mathit{r}\mathit{u}\mathit{c}(\mathit{\_}\mathit{a},[\{\left(\frac{\mathrm{d}}{\mathrm{d}\mathit{\_}\mathit{a}}\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)-\frac{1}{n^2}(2{\mathit{\_}\mathit{a}}^{\frac{n}{n+1}}\mathit{\_}\mathit{a}{n}^2+3\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)n^2+6{\mathit{\_}\mathit{a}}^{\frac{n}{n+1}}\mathit{\_}\mathit{a}n-2\mathit{\_}\mathit{a}{n}^2+4\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)n+4{\mathit{\_}\mathit{a}}^{\frac{n}{n+1}}\mathit{\_}\mathit{a}-6\mathit{\_}\mathit{a}n-4\mathit{\_}\mathit{a})=0\},\{\mathit{\_}\mathit{a}=y\left(x\right),\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)=\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\},\{x=\int {\left(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)}^{-1}\mathrm{d}\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1},y\left(x\right)=\mathit{\_}\mathit{a}\}])\}$$