4.405   ODE No. 1405

$$\boxed{{\displaystyle \frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)=\frac{(2x^2+1)\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)}{x^3}-1/4\frac{(a{x}^4+10x^2+1)y\left(x\right)}{x^6}=0}}$$

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

Mathematica: cpu = 0.075510 (sec), leaf count = 77 $$\left\{\{y(x)\to c_1{e}^{-\frac{1}{4x^2}}{x}^{\frac{3}{2}-\frac{\sqrt{9-a}}{2}}+\frac{c_2{e}^{-\frac{1}{4x^2}}{x}^{\frac{\sqrt{9-a}}{2}+\frac{3}{2}}}{\sqrt{9-a}}\}\right\}$$

Maple: cpu = 0.062 (sec), leaf count = 47 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{x}^{\frac{3}{2}+\frac{1}{2}\sqrt{-a+9}}{\mathrm{e}}^{-\frac{1}{4x^2}}+\mathit{\_}\mathit{C}\mathit{2}{x}^{\frac{3}{2}-\frac{1}{2}\sqrt{-a+9}}{\mathrm{e}}^{-\frac{1}{4x^2}}\}$$