8.32   ODE No. 1622

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

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

Mathematica: cpu = 26.601378 (sec), leaf count = 41 $$\text{DSolve}[2a^{2}y(x)+(3a+y(x))y^{\prime }(x)+ay(x{)}^2+y^{″}(x)-y(x{)}^3=0,y(x),x]$$

Maple: cpu = 0.219 (sec), leaf count = 775 $$\{y\left(x\right)=\frac{1}{{\mathrm{e}}^{ax}}\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}({\int }^{\mathit{\_}\mathit{Z}}\frac{1}{-{\mathit{\_}\mathit{f}}^6+\mathit{\_}\mathit{C}\mathit{1}}({\mathit{\_}\mathit{f}}^8-\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{f}}^2+{(-{\mathit{\_}\mathit{f}}^{12}+2\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{f}}^6-{\mathit{\_}\mathit{C}\mathit{1}}^2+\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{f}}^6+\mathit{\_}\mathit{C}\mathit{1}}}{\mathit{\_}\mathit{f}}^{12}-2\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{f}}^6+\mathit{\_}\mathit{C}\mathit{1}}}\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{f}}^6+\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{f}}^6+\mathit{\_}\mathit{C}\mathit{1}}}{\mathit{\_}\mathit{C}\mathit{1}}^2)}^{\frac{2}{3}})\frac{1}{\sqrt[3]{-{\mathit{\_}\mathit{f}}^{12}+2\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{f}}^6-{\mathit{\_}\mathit{C}\mathit{1}}^2+\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{f}}^6+\mathit{\_}\mathit{C}\mathit{1}}}{\mathit{\_}\mathit{f}}^{12}-2\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{f}}^6+\mathit{\_}\mathit{C}\mathit{1}}}\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{f}}^6+\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{f}}^6+\mathit{\_}\mathit{C}\mathit{1}}}{\mathit{\_}\mathit{C}\mathit{1}}^2}}d\mathit{\_}\mathit{f}a+\mathit{\_}\mathit{C}\mathit{2}a+{\mathrm{e}}^{-ax}),y\left(x\right)=\frac{1}{{\mathrm{e}}^{ax}}\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}({\int }^{\mathit{\_}\mathit{Z}}\frac{1}{-{\mathit{\_}\mathit{f}}^6+\mathit{\_}\mathit{C}\mathit{1}}(-i\sqrt{3}{\mathit{\_}\mathit{f}}^8-{\mathit{\_}\mathit{f}}^8+i\sqrt{3}\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{f}}^2+i\sqrt{3}{(-{\mathit{\_}\mathit{f}}^{12}+2\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{f}}^6-{\mathit{\_}\mathit{C}\mathit{1}}^2+\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{f}}^6+\mathit{\_}\mathit{C}\mathit{1}}}{\mathit{\_}\mathit{f}}^{12}-2\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{f}}^6+\mathit{\_}\mathit{C}\mathit{1}}}\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{f}}^6+\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{f}}^6+\mathit{\_}\mathit{C}\mathit{1}}}{\mathit{\_}\mathit{C}\mathit{1}}^2)}^{\frac{2}{3}}+\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{f}}^2-{(-{\mathit{\_}\mathit{f}}^{12}+2\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{f}}^6-{\mathit{\_}\mathit{C}\mathit{1}}^2+\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{f}}^6+\mathit{\_}\mathit{C}\mathit{1}}}{\mathit{\_}\mathit{f}}^{12}-2\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{f}}^6+\mathit{\_}\mathit{C}\mathit{1}}}\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{f}}^6+\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{f}}^6+\mathit{\_}\mathit{C}\mathit{1}}}{\mathit{\_}\mathit{C}\mathit{1}}^2)}^{\frac{2}{3}})\frac{1}{\sqrt[3]{-{\mathit{\_}\mathit{f}}^{12}+2\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{f}}^6-{\mathit{\_}\mathit{C}\mathit{1}}^2+\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{f}}^6+\mathit{\_}\mathit{C}\mathit{1}}}{\mathit{\_}\mathit{f}}^{12}-2\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{f}}^6+\mathit{\_}\mathit{C}\mathit{1}}}\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{f}}^6+\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{f}}^6+\mathit{\_}\mathit{C}\mathit{1}}}{\mathit{\_}\mathit{C}\mathit{1}}^2}}d\mathit{\_}\mathit{f}a+2\mathit{\_}\mathit{C}\mathit{2}a+2{\mathrm{e}}^{-ax}),y\left(x\right)=\frac{1}{{\mathrm{e}}^{ax}}\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-{\int }^{\mathit{\_}\mathit{Z}}\frac{1}{-{\mathit{\_}\mathit{f}}^6+\mathit{\_}\mathit{C}\mathit{1}}(-i\sqrt{3}{\mathit{\_}\mathit{f}}^8+{\mathit{\_}\mathit{f}}^8+i\sqrt{3}\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{f}}^2+i\sqrt{3}{(-{\mathit{\_}\mathit{f}}^{12}+2\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{f}}^6-{\mathit{\_}\mathit{C}\mathit{1}}^2+\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{f}}^6+\mathit{\_}\mathit{C}\mathit{1}}}{\mathit{\_}\mathit{f}}^{12}-2\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{f}}^6+\mathit{\_}\mathit{C}\mathit{1}}}\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{f}}^6+\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{f}}^6+\mathit{\_}\mathit{C}\mathit{1}}}{\mathit{\_}\mathit{C}\mathit{1}}^2)}^{\frac{2}{3}}-\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{f}}^2+{(-{\mathit{\_}\mathit{f}}^{12}+2\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{f}}^6-{\mathit{\_}\mathit{C}\mathit{1}}^2+\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{f}}^6+\mathit{\_}\mathit{C}\mathit{1}}}{\mathit{\_}\mathit{f}}^{12}-2\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{f}}^6+\mathit{\_}\mathit{C}\mathit{1}}}\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{f}}^6+\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{f}}^6+\mathit{\_}\mathit{C}\mathit{1}}}{\mathit{\_}\mathit{C}\mathit{1}}^2)}^{\frac{2}{3}})\frac{1}{\sqrt[3]{-{\mathit{\_}\mathit{f}}^{12}+2\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{f}}^6-{\mathit{\_}\mathit{C}\mathit{1}}^2+\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{f}}^6+\mathit{\_}\mathit{C}\mathit{1}}}{\mathit{\_}\mathit{f}}^{12}-2\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{f}}^6+\mathit{\_}\mathit{C}\mathit{1}}}\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{f}}^6+\sqrt{\frac{\mathit{\_}\mathit{C}\mathit{1}}{-{\mathit{\_}\mathit{f}}^6+\mathit{\_}\mathit{C}\mathit{1}}}{\mathit{\_}\mathit{C}\mathit{1}}^2}}d\mathit{\_}\mathit{f}a+2\mathit{\_}\mathit{C}\mathit{2}a+2{\mathrm{e}}^{-ax})\}$$