3.40   ODE No. 40

$$\boxed{{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+3a{\left(y\left(x\right)\right)}^3+6ax{\left(y\left(x\right)\right)}^2=0}}$$

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

Mathematica: cpu = 0.241531 (sec), leaf count = 185 $$\text{Solve}[\frac{\sqrt[3]{-3}\sqrt[3]{a}x\text{Ai}((-3{)}^{2/3}{a}^{2/3}{x}^2-\frac{(-1{)}^{2/3}}{\sqrt[3]{3}\sqrt[3]{a}y(x)})+{\text{Ai}}^{\prime }((-3{)}^{2/3}{a}^{2/3}{x}^2-\frac{(-1{)}^{2/3}}{\sqrt[3]{3}\sqrt[3]{a}y(x)})}{\sqrt[3]{-3}\sqrt[3]{a}x\text{Bi}((-3{)}^{2/3}{a}^{2/3}{x}^2-\frac{(-1{)}^{2/3}}{\sqrt[3]{3}\sqrt[3]{a}y(x)})+{\text{Bi}}^{\prime }((-3{)}^{2/3}{a}^{2/3}{x}^2-\frac{(-1{)}^{2/3}}{\sqrt[3]{3}\sqrt[3]{a}y(x)})}+c_1=0,y(x)]$$

Maple: cpu = 0.062 (sec), leaf count = 48 $$\{y\left(x\right)={(3a{x}^2+\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(\sqrt[3]{-3a}\mathrm{B}\mathrm{i}\left(\mathit{\_}\mathit{Z}\right)\mathit{\_}\mathit{C}\mathit{1}x+\sqrt[3]{-3a}x\mathrm{A}\mathrm{i}\left(\mathit{\_}\mathit{Z}\right)+{\mathrm{B}\mathrm{i}}^{(1)}\left(\mathit{\_}\mathit{Z}\right)\mathit{\_}\mathit{C}\mathit{1}+{\mathrm{A}\mathrm{i}}^{(1)}\left(\mathit{\_}\mathit{Z}\right))\sqrt[3]{-3a})}^{-1}\}$$

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