4.353   ODE No. 1353

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

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

Mathematica: cpu = 0.107514 (sec), leaf count = 119 $$\left\{\{y(x)\to c_1(x^3+2x-\frac{1}{x})-\frac{c_2(\sqrt{2\pi }{x}^4\text{erfi}\left(\frac{1}{\sqrt{2}x}\right)+2\sqrt{2\pi }{x}^2\text{erfi}\left(\frac{1}{\sqrt{2}x}\right)-\sqrt{2\pi }\text{erfi}\left(\frac{1}{\sqrt{2}x}\right)+2e^{\frac{1}{2x^2}}x-2e^{\frac{1}{2x^2}}{x}^3)}{16x}\}\right\}$$

Maple: cpu = 0.141 (sec), leaf count = 68 $$\{y\left(x\right)=\frac{\mathit{\_}\mathit{C}\mathit{1}}{x}(\sqrt{2}\sqrt{\pi }(x^4+2x^2-1)\mathit{e}\mathit{r}\mathit{f}\mathit{i}\left(\frac{\sqrt{2}}{2x}\right)+(-2x^3+2x){\mathrm{e}}^{\frac{1}{2x^2}})+\frac{\mathit{\_}\mathit{C}\mathit{2}(x^4+2x^2-1)}{x}\}$$