5.58   ODE No. 1506

$$\boxed{{\displaystyle 4x^2\frac{{\mathrm{d}}^3}{\mathrm{d}{x}^3}y\left(x\right)+(x^2+14x-1)\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)+4(1+x)\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+2y\left(x\right)=0}}$$

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

Mathematica: cpu = 30.884422 (sec), leaf count = 208 $$\left\{\{y(x)\to c_2(-\sqrt{e\pi }\text{erfi}\left(\frac{x-1}{2\sqrt{x}}\right)+3\sqrt{\frac{\pi }{e}}\text{erfi}\left(\frac{x+1}{2\sqrt{x}}\right)-3\sqrt{\frac{\pi }{e}}\text{erfi}(1)-\frac{4e^{\frac{x^2+1}{4x}}}{\sqrt{x}}+4\sqrt{e})e^{\frac{1}{4}(-x-\frac{1}{x}+2\log (x))}-\sqrt{\pi }{c}_3(e\text{erfi}\left(\frac{1-x}{2\sqrt{x}}\right)+\text{erfi}\left(\frac{x+1}{2\sqrt{x}}\right)-i(e-1))e^{\frac{1}{4}(-x-\frac{1}{x}+2\log (x))-\frac{1}{2}}+c_1{e}^{\frac{1}{4}(-x-\frac{1}{x}+2\log (x))}\}\right\}$$

Maple: cpu = 0.031 (sec), leaf count = 43 $$\{y\left(x\right)=(\mathit{\_}\mathit{C}\mathit{3}+\int \frac{2x\mathit{\_}\mathit{C}\mathit{1}+\mathit{\_}\mathit{C}\mathit{2}}{4}{\mathrm{e}}^{\frac{x}{4}}{\mathrm{e}}^{\frac{1}{4x}}{x}^{-\frac{5}{2}}\mathrm{d}x){\mathrm{e}}^{-\frac{x}{4}}\sqrt{x}{\mathrm{e}}^{-\frac{1}{4x}}\}$$