4.401   ODE No. 1401

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

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

Mathematica: cpu = 0.013002 (sec), leaf count = 93 $$\left\{\{y(x)\to c_1{e}^{-\frac{\sqrt{b}(-\frac{\sqrt{a^2-4b}}{\sqrt{b}}-\frac{a}{\sqrt{b}})}{4x^2}}+c_2{e}^{-\frac{\sqrt{b}(\frac{\sqrt{a^2-4b}}{\sqrt{b}}-\frac{a}{\sqrt{b}})}{4x^2}}\}\right\}$$

Maple: cpu = 0.047 (sec), leaf count = 45 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{-\frac{1}{4x^2}(-a+\sqrt{a^2-4b})}+\mathit{\_}\mathit{C}\mathit{2}{\mathrm{e}}^{\frac{1}{4x^2}(a+\sqrt{a^2-4b})}\}$$