3.44   ODE No. 44

$$\boxed{{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+2a{x}^3{\left(y\left(x\right)\right)}^3+2xy\left(x\right)=0}}$$

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

Mathematica: cpu = 0.014502 (sec), leaf count = 72 $$\{\{y(x)\to -\frac{\sqrt{2}}{\sqrt{-2a{x}^2-a+2c_1{e}^{2x^2}}}\},\{y(x)\to \frac{\sqrt{2}}{\sqrt{-2a{x}^2-a+2c_1{e}^{2x^2}}}\}\}$$

Maple: cpu = 0.016 (sec), leaf count = 53 $$\{y\left(x\right)=-2\frac{1}{\sqrt{-4a{x}^2+4{\mathrm{e}}^{2x^2}\mathit{\_}\mathit{C}\mathit{1}-2a}},y\left(x\right)=2\frac{1}{\sqrt{-4a{x}^2+4{\mathrm{e}}^{2x^2}\mathit{\_}\mathit{C}\mathit{1}-2a}}\}$$

Sage: cpu = 0.9 (sec), leaf count = 0 $$[\frac{e^{(-x^2)}}{\sqrt{-\frac{1}{2}(2x^2+1)a{e}^{(-2x^2)}+c}},\mathtt{\text{bernoulli}}]$$