3.815   ODE No. 815

$$\boxed{{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)=\frac{{(3+y\left(x\right))}^3{\mathrm{e}}^{9/2x^2}x{\mathrm{e}}^{3/2x^2}}{(243{\mathrm{e}}^{3/2x^2}+81{\mathrm{e}}^{3/2x^2}y\left(x\right)+243y\left(x\right)){\mathrm{e}}^{3x^2}}=0}}$$

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

Mathematica: cpu = 10.172792 (sec), leaf count = 103 $$\text{Solve}[\frac{1}{186}(31\log (-81e^{\frac{3x^2}{2}}(y(x)+3)y(x)+e^{3x^2}(y(x)+3{)}^2-243y(x{)}^2)-6\sqrt{93}{\tanh }^{-1}\left(\frac{2e^{\frac{3x^2}{2}}(y(x)+3)-81y(x)}{9\sqrt{93}y(x)}\right))-\frac{1}{3}\log (y(x)+3)=c_1,y(x)]$$

Maple: cpu = 1.326 (sec), leaf count = 202 $$\{5\ln \left(\frac{100{\left({\mathrm{e}}^{3/2x^2}\right)}^2{\left(y\left(x\right)\right)}^2+600{\left({\mathrm{e}}^{3/2x^2}\right)}^{2}y\left(x\right)-8100{\left(y\left(x\right)\right)}^2{\mathrm{e}}^{3/2x^2}+900{\left({\mathrm{e}}^{3/2x^2}\right)}^2-24300{\mathrm{e}}^{3/2x^2}y\left(x\right)-24300{\left(y\left(x\right)\right)}^2}{189{(3{\mathrm{e}}^{3/2x^2}+{\mathrm{e}}^{3/2x^2}y\left(x\right)+3y\left(x\right))}^2}\right)-\frac{30\sqrt{93}}{31}\mathit{A}\mathit{r}\mathit{t}\mathit{a}\mathit{n}\mathit{h}\left(\frac{\sqrt{93}}{279}(29{\mathrm{e}}^{3/2x^2}y\left(x\right)+87{\mathrm{e}}^{3/2x^2}+81y\left(x\right)){(3{\mathrm{e}}^{3/2x^2}+{\mathrm{e}}^{\frac{3x^2}{2}}y\left(x\right)+3y\left(x\right))}^{-1}\right)-10\ln \left(\frac{10{\mathrm{e}}^{3/2x^2}(3+y\left(x\right))}{27{\mathrm{e}}^{3/2x^2}+9{\mathrm{e}}^{3/2x^2}y\left(x\right)+27y\left(x\right)}\right)+15x^2-\mathit{\_}\mathit{C}\mathit{1}=0\}$$