2.815   ODE No. 815

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

$$y^{\prime }(x)=\frac{e^{3x^2}x(y(x)+3{)}^3}{81(e^{\frac{3x^2}{2}}y(x)+3e^{\frac{3x^2}{2}}+3y(x))}$$ ✓ Mathematica : cpu = 18.1846 (sec), leaf count = 100

$$\text{Solve}[\frac{1}{6}(\log (-81e^{\frac{3x^2}{2}}(y(x)+3)y(x)+e^{3x^2}(y(x)+3{)}^2-243y(x{)}^2)-2\log (y(x)+3))=c_1+\sqrt{\frac{3}{31}}{\tanh }^{-1}\left(\frac{2e^{\frac{3x^2}{2}}(y(x)+3)-81y(x)}{9\sqrt{93}y(x)}\right),y(x)]$$

✓ Maple : cpu = 0.829 (sec), leaf count = 168

$$\{5\ln \left(\frac{100{(3+y\left(x\right))}^2{\left({\mathrm{e}}^{3/2x^2}\right)}^2+(-8100{\left(y\left(x\right)\right)}^2-24300y\left(x\right)){\mathrm{e}}^{3/2x^2}-24300{\left(y\left(x\right)\right)}^2}{189{({\mathrm{e}}^{3/2x^2}(3+y\left(x\right))+3y\left(x\right))}^2}\right)-\frac{30\sqrt{93}}{31}\mathit{A}\mathit{r}\mathit{t}\mathit{a}\mathit{n}\mathit{h}\left(\sqrt{93}(29{\mathrm{e}}^{3/2x^2}y\left(x\right)+87{\mathrm{e}}^{3/2x^2}+81y\left(x\right)){((279y\left(x\right)+837){\mathrm{e}}^{\frac{3x^2}{2}}+837y\left(x\right))}^{-1}\right)-10\ln \left(\frac{10{\mathrm{e}}^{3/2x^2}(3+y\left(x\right))}{27{\mathrm{e}}^{3/2x^2}+9{\mathrm{e}}^{3/2x^2}y\left(x\right)+27y\left(x\right)}\right)+15x^2-\mathit{\_}\mathit{C}\mathit{1}=0\}$$