4.106   ODE No. 1106

$$\boxed{{\displaystyle x\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)+a\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+b{x}^{\mathit{a}\mathit{1}}y\left(x\right)=0}}$$

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

Mathematica: cpu = 0.054507 (sec), leaf count = 447 $$\left\{\{y(x)\to c_1{(\frac{1}{\text{a1}}+1)}^{\frac{a}{(\frac{1}{\text{a1}}+1)\text{a1}}-\frac{1}{(\frac{1}{\text{a1}}+1)\text{a1}}}{\text{a1}}^{\frac{a}{(\frac{1}{\text{a1}}+1)\text{a1}}-\frac{1}{(\frac{1}{\text{a1}}+1)\text{a1}}}{b}^{\frac{1}{2}(\frac{1}{(\frac{1}{\text{a1}}+1)\text{a1}}-\frac{a}{(\frac{1}{\text{a1}}+1)\text{a1}})}{\left(x^{\text{a1}}\right)}^{(\frac{1}{2\text{a1}}+\frac{1}{2})(\frac{1}{(\frac{1}{\text{a1}}+1)\text{a1}}-\frac{a}{(\frac{1}{\text{a1}}+1)\text{a1}})}\mathrm{\Gamma }(\frac{a}{\text{a1}+1}+\frac{\text{a1}}{\text{a1}+1})J_{\frac{a-1}{\text{a1}+1}}\left(\frac{2\sqrt{b}{\left(x^{\text{a1}}\right)}^{\frac{1}{2}(1+\frac{1}{\text{a1}})}}{(1+\frac{1}{\text{a1}})\text{a1}}\right)+c_2{(\frac{1}{\text{a1}}+1)}^{-\frac{2(1-a)}{\text{a1}+1}-\frac{a}{(\frac{1}{\text{a1}}+1)\text{a1}}+\frac{1}{(\frac{1}{\text{a1}}+1)\text{a1}}}{\text{a1}}^{-\frac{2(1-a)}{\text{a1}+1}-\frac{a}{(\frac{1}{\text{a1}}+1)\text{a1}}+\frac{1}{(\frac{1}{\text{a1}}+1)\text{a1}}}{b}^{\frac{1-a}{\text{a1}+1}+\frac{1}{2}(\frac{a}{(\frac{1}{\text{a1}}+1)\text{a1}}-\frac{1}{(\frac{1}{\text{a1}}+1)\text{a1}})}{\left(x^{\text{a1}}\right)}^{\frac{(1-a)(\frac{1}{\text{a1}}+1)}{\text{a1}+1}+(\frac{1}{2\text{a1}}+\frac{1}{2})(\frac{a}{(\frac{1}{\text{a1}}+1)\text{a1}}-\frac{1}{(\frac{1}{\text{a1}}+1)\text{a1}})}\mathrm{\Gamma }(-\frac{a}{\text{a1}+1}+\frac{\text{a1}}{\text{a1}+1}+\frac{2}{\text{a1}+1})J_{\frac{1-a}{\text{a1}+1}}\left(\frac{2\sqrt{b}{\left(x^{\text{a1}}\right)}^{\frac{1}{2}(1+\frac{1}{\text{a1}})}}{(1+\frac{1}{\text{a1}})\text{a1}}\right)\}\right\}$$

Maple: cpu = 0.062 (sec), leaf count = 77 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{x}^{-\frac{a}{2}+\frac{1}{2}}{\mathit{J}}_{\frac{a-1}{\mathit{a}\mathit{1}+1}}\left(2\frac{\sqrt{b}{x}^{\mathit{a}\mathit{1}/2+1/2}}{\mathit{a}\mathit{1}+1}\right)+\mathit{\_}\mathit{C}\mathit{2}{x}^{-\frac{a}{2}+\frac{1}{2}}{\mathit{Y}}_{\frac{a-1}{\mathit{a}\mathit{1}+1}}\left(2\frac{\sqrt{b}{x}^{\mathit{a}\mathit{1}/2+1/2}}{\mathit{a}\mathit{1}+1}\right)\}$$