3.31   ODE No. 31

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

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

Mathematica: cpu = 0.060008 (sec), leaf count = 21 $$\left\{\{y(x)\to \tan (\frac{a{x}^{n+1}}{n+1}+c_1)\}\right\}$$

Maple: cpu = 0.031 (sec), leaf count = 26 $$\{y\left(x\right)=\tan \left(\frac{\mathit{\_}\mathit{C}\mathit{1}an+x^{n+1}a+\mathit{\_}\mathit{C}\mathit{1}a}{n+1}\right)\}$$

Sage: cpu = 0 (sec), leaf count = 0 $$\text{Maxima was unable to solve this ODE}$$