3.796   ODE No. 796

$$\boxed{{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)=1/3\frac{x{\left(y\left(x\right)\right)}^3{\mathrm{e}}^{3x^2}}{(3{\mathrm{e}}^{3/2x^2}+{\mathrm{e}}^{3/2x^2}y\left(x\right)+3y\left(x\right)){\mathrm{e}}^{9/2x^2}}=0}}$$

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

Mathematica: cpu = 9.404194 (sec), leaf count = 102 $$\text{Solve}[\frac{1}{62}(-31\log (9e^{\frac{3x^2}{2}}(y(x)+3)y(x)+3e^{3x^2}(y(x)+3{)}^2-y(x{)}^2)+6\sqrt{93}{\tanh }^{-1}\left(\frac{\sqrt{\frac{3}{31}}(2e^{\frac{3x^2}{2}}(y(x)+3)+3y(x))}{y(x)}\right)+93x^2)+\log (y(x))=c_1,y(x)]$$

Maple: cpu = 1.155 (sec), leaf count = 143 $$\{y\left(x\right)=\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}((7{\mathrm{e}}^{3x^2+\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}\left({\left({\mathrm{e}}^{3/2x^2}\right)}^2(42\sqrt{93}\tanh \left(\frac{(\mathit{\_}\mathit{C}\mathit{1}-5\mathit{\_}\mathit{Z})\sqrt{93}}{90}\right){\mathrm{e}}^{3x^2+\mathit{\_}\mathit{Z}}+217{(\tanh \left(\frac{(\mathit{\_}\mathit{C}\mathit{1}-5\mathit{\_}\mathit{Z})\sqrt{93}}{90}\right))}^2{\mathrm{e}}^{3x^2+\mathit{\_}\mathit{Z}}+189{\mathrm{e}}^{3x^2+\mathit{\_}\mathit{Z}}-93{(\tanh \left(\frac{(\mathit{\_}\mathit{C}\mathit{1}-5\mathit{\_}\mathit{Z})\sqrt{93}}{90}\right))}^2+93)\right)}+9{\left({\mathrm{e}}^{3/2x^2}\right)}^2+27{\mathrm{e}}^{3/2x^2}-3){\mathit{\_}\mathit{Z}}^2+81+(54{\mathrm{e}}^{3/2x^2}+81)\mathit{\_}\mathit{Z}){\mathrm{e}}^{\frac{3x^2}{2}}\}$$