5.66   ODE No. 1514

$$\boxed{{\displaystyle x^3\frac{{\mathrm{d}}^3}{\mathrm{d}{x}^3}y\left(x\right)+6x^2\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)+(a{x}^3-12)y\left(x\right)=0}}$$

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

Mathematica: cpu = 0.717091 (sec), leaf count = 102 $$\left\{\{y(x)\to \frac{c_1{e}^{-\sqrt[3]{a}x}(\sqrt[3]{a}x+2)}{x^3}+\frac{c_2{e}^{\sqrt[3]{-1}\sqrt[3]{a}x}(\sqrt[3]{a}x+2(-1{)}^{2/3})}{x^3}+\frac{c_3{e}^{-(-1{)}^{2/3}\sqrt[3]{a}x}(\sqrt[3]{a}x-2\sqrt[3]{-1})}{x^3}\}\right\}$$

Maple: cpu = 0.390 (sec), leaf count = 151 $$\{y\left(x\right)=\frac{\mathit{\_}\mathit{C}\mathit{1}}{x^3}(a^{3}x+2{(-a^4)}^{2/3}){\mathrm{e}}^{\frac{x}{a}\sqrt[3]{-a^4}}+\frac{\mathit{\_}\mathit{C}\mathit{2}}{x^3}({(-a^4)}^{\frac{2}{3}}\sqrt{3}-i{a}^{3}x+i{(-a^4)}^{\frac{2}{3}}){\mathrm{e}}^{\frac{\frac{i}{2}(-\sqrt{3}+i)x}{a}\sqrt[3]{-a^4}}+\frac{\mathit{\_}\mathit{C}\mathit{3}}{x^3}(-i{a}^{3}x+i{(-a^4)}^{\frac{2}{3}}-{(-a^4)}^{\frac{2}{3}}\sqrt{3}){\mathrm{e}}^{\frac{\frac{i}{2}(\sqrt{3}+i)x}{a}\sqrt[3]{-a^4}}\}$$