2.1546   ODE No. 1546

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

$$a^4{x}^{4}y(x)+4a^3{x}^3{y}^{\prime }(x)+6a^2{x}^2{y}^{″}(x)+4ax{y}^{(3)}(x)+y^{(4)}(x)=0$$ ✓ Mathematica : cpu = 0.671423 (sec), leaf count = 301

$$\left\{\{y(x)\to \frac{2(\sqrt{6}-3)\sqrt{-(\sqrt{6}-3)a}{c}_3\exp (-\frac{a{x}^2}{2}-\sqrt{-(\sqrt{6}-3)a}x-\frac{(-3+\sqrt{3}+\sqrt{6})ax}{\sqrt{-(\sqrt{6}-3)a}})}{(-3-\sqrt{3}+\sqrt{6})(-3+\sqrt{3}+\sqrt{6})a}+\frac{2(\sqrt{6}-3)\sqrt{-(\sqrt{6}-3)a}{c}_4\exp (-\frac{a{x}^2}{2}-\sqrt{-(\sqrt{6}-3)a}x-\frac{(-3-\sqrt{3}+\sqrt{6})ax}{\sqrt{-(\sqrt{6}-3)a}})}{(-3-\sqrt{3}+\sqrt{6})(-3+\sqrt{3}+\sqrt{6})a}+c_1{e}^{-\frac{a{x}^2}{2}-\sqrt{-(\sqrt{6}-3)a}x}+c_2{e}^{\sqrt{-(\sqrt{6}-3)a}x-\frac{a{x}^2}{2}}\}\right\}$$

✓ Maple : cpu = 0.052 (sec), leaf count = 81

$$\{y\left(x\right)={\mathrm{e}}^{-\frac{a{x}^2}{2}}(\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{-\sqrt{-a\sqrt{6}+3a}x}+\mathit{\_}\mathit{C}\mathit{2}{\mathrm{e}}^{\sqrt{-a\sqrt{6}+3a}x}+\mathit{\_}\mathit{C}\mathit{3}{\mathrm{e}}^{-\sqrt{a\sqrt{6}+3a}x}+\mathit{\_}\mathit{C}\mathit{4}{\mathrm{e}}^{\sqrt{a\sqrt{6}+3a}x})\}$$