4.349   ODE No. 1349

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

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

Mathematica: cpu = 0.087011 (sec), leaf count = 76 $$\left\{\{y(x)\to c_2{G}_{1,2}^{2,0}(-\frac{1}{2x^2}|\begin{array}{c}\frac{3}{2}\\ 0,0\end{array})+c_1{e}^{\frac{1}{4x^2}}((1-\frac{1}{2x^2})I_0\left(\frac{1}{4x^2}\right)+\frac{I_1\left(\frac{1}{4x^2}\right)}{2x^2})\}\right\}$$

Maple: cpu = 0.063 (sec), leaf count = 73 $$\{y\left(x\right)=\frac{\mathit{\_}\mathit{C}\mathit{1}}{x^2}{\mathrm{e}}^{\frac{1}{4x^2}}((2x^2-1){\mathit{I}}_0\left(\frac{1}{4x^2}\right)+{\mathit{I}}_1\left(\frac{1}{4x^2}\right))+\frac{\mathit{\_}\mathit{C}\mathit{2}}{x^2}{\mathrm{e}}^{\frac{1}{4x^2}}((2x^2-1){\mathit{K}}_0(-\frac{1}{4x^2})+{\mathit{K}}_1(-\frac{1}{4x^2}))\}$$