4.195   ODE No. 1195

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

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

Mathematica: cpu = 0.028004 (sec), leaf count = 80 $$\left\{\{y(x)\to c_{1}U(2+\sqrt{2},1+2\sqrt{2},x)e^{(\sqrt{2}-1)\log (x)-x}+c_2{L}_{-2-\sqrt{2}}^{2\sqrt{2}}(x)e^{(\sqrt{2}-1)\log (x)-x}\}\right\}$$

Maple: cpu = 0.078 (sec), leaf count = 94 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{-\frac{x}{2}}((\sqrt{2}+x+1){\mathit{I}}_{-\frac{1}{2}+\sqrt{2}}\left(\frac{x}{2}\right)+(-\sqrt{2}+x+1){\mathit{I}}_{\frac{1}{2}+\sqrt{2}}\left(\frac{x}{2}\right))\frac{1}{\sqrt{x}}+\mathit{\_}\mathit{C}\mathit{2}{\mathrm{e}}^{-\frac{x}{2}}((\sqrt{2}+x+1){\mathit{K}}_{-\frac{1}{2}+\sqrt{2}}\left(\frac{x}{2}\right)-{\mathit{K}}_{\frac{1}{2}+\sqrt{2}}\left(\frac{x}{2}\right)(-\sqrt{2}+x+1))\frac{1}{\sqrt{x}}\}$$