3.316   ODE No. 316

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

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

Mathematica: cpu = 0.039005 (sec), leaf count = 48 $$\{\{y(x)\to 0\},\text{Solve}[x=c_1{e}^{-\frac{1}{2}y(x{)}^2}-\frac{1}{4}{e}^{-\frac{1}{2}y(x{)}^2}\text{Ei}\left(\frac{y(x{)}^2}{2}\right),y(x)]\}$$

Maple: cpu = 0.047 (sec), leaf count = 53 $$\{y\left(x\right)=0,y\left(x\right)=\sqrt{-2\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}({\mathrm{e}}^{\mathit{\_}\mathit{Z}}\mathit{E}\mathit{i}(1,\mathit{\_}\mathit{Z})+4{\mathrm{e}}^{\mathit{\_}\mathit{Z}}\mathit{\_}\mathit{C}\mathit{1}-4x)},y\left(x\right)=-\sqrt{-2\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}({\mathrm{e}}^{\mathit{\_}\mathit{Z}}\mathit{E}\mathit{i}(1,\mathit{\_}\mathit{Z})+4{\mathrm{e}}^{\mathit{\_}\mathit{Z}}\mathit{\_}\mathit{C}\mathit{1}-4x)}\}$$