2.1195   ODE No. 1195

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

$$x^2{y}^{″}(x)+(x+3)x{y}^{\prime }(x)-y(x)=0$$ ✓ Mathematica : cpu = 0.0299838 (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 = 0.122 (sec), leaf count = 94

$$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{-\frac{x}{2}}((\sqrt{2}+x+1){\mathit{I}}_{-\frac{1}{2}+\sqrt{2}}\left(\frac{x}{2}\right)+(-\sqrt{2}+x+1){\mathit{I}}_{\frac{1}{2}+\sqrt{2}}\left(\frac{x}{2}\right))\frac{1}{\sqrt{x}}+\mathit{\_}\mathit{C}\mathit{2}((\sqrt{2}+x+1){\mathit{K}}_{-\frac{1}{2}+\sqrt{2}}\left(\frac{x}{2}\right)-{\mathit{K}}_{\frac{1}{2}+\sqrt{2}}\left(\frac{x}{2}\right)(-\sqrt{2}+x+1)){\mathrm{e}}^{-\frac{x}{2}}\frac{1}{\sqrt{x}}\}$$