2.1615   ODE No. 1615

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

$$-\frac{2(n+1)(n+2)y(x)(y(x{)}^{\frac{n}{n+1}}-1)}{n^2}-\frac{(3n+4)y^{\prime }(x)}{n}+y^{″}(x)=0$$ ✗ Mathematica : cpu = 75.3693 (sec), leaf count = 0 , could not solve

DSolve[(-2*(1 + n)*(2 + n)*y[x]*(-1 + y[x]^(n/(1 + n))))/n^2 - ((4 + 3*n)*Derivative[1][y][x])/n + Derivative[2][y][x] == 0, y[x], x]

✓ Maple : cpu = 12.922 (sec), leaf count = 91

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