2.1106   ODE No. 1106

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

$$a{y}^{\prime }(x)+b{x}^{\text{a1}}y(x)+x{y}^{″}(x)=0$$ ✓ Mathematica : cpu = 0.0394293 (sec), leaf count = 441

$$\left\{\{y(x)\to c_1{(\frac{1}{\text{a1}}+1)}^{\frac{a}{(\frac{1}{\text{a1}}+1)\text{a1}}-\frac{1}{(\frac{1}{\text{a1}}+1)\text{a1}}}{\text{a1}}^{\frac{a}{(\frac{1}{\text{a1}}+1)\text{a1}}-\frac{1}{(\frac{1}{\text{a1}}+1)\text{a1}}}{b}^{\frac{1}{2}(\frac{1}{(\frac{1}{\text{a1}}+1)\text{a1}}-\frac{a}{(\frac{1}{\text{a1}}+1)\text{a1}})}{\left(x^{\text{a1}}\right)}^{\frac{1}{2}(\frac{1}{\text{a1}}+1)(\frac{1}{(\frac{1}{\text{a1}}+1)\text{a1}}-\frac{a}{(\frac{1}{\text{a1}}+1)\text{a1}})}\mathrm{\Gamma }(\frac{a}{\text{a1}+1}+\frac{\text{a1}}{\text{a1}+1})J_{\frac{a-1}{\text{a1}+1}}\left(\frac{2\sqrt{b}{\left(x^{\text{a1}}\right)}^{\frac{1}{2}(1+\frac{1}{\text{a1}})}}{(1+\frac{1}{\text{a1}})\text{a1}}\right)+c_2{(\frac{1}{\text{a1}}+1)}^{-\frac{2(1-a)}{\text{a1}+1}-\frac{a}{(\frac{1}{\text{a1}}+1)\text{a1}}+\frac{1}{(\frac{1}{\text{a1}}+1)\text{a1}}}{\text{a1}}^{-\frac{2(1-a)}{\text{a1}+1}-\frac{a}{(\frac{1}{\text{a1}}+1)\text{a1}}+\frac{1}{(\frac{1}{\text{a1}}+1)\text{a1}}}{b}^{\frac{1-a}{\text{a1}+1}+\frac{1}{2}(\frac{a}{(\frac{1}{\text{a1}}+1)\text{a1}}-\frac{1}{(\frac{1}{\text{a1}}+1)\text{a1}})}{\left(x^{\text{a1}}\right)}^{\frac{1}{2}(\frac{1}{\text{a1}}+1)(\frac{a}{(\frac{1}{\text{a1}}+1)\text{a1}}-\frac{1}{(\frac{1}{\text{a1}}+1)\text{a1}})+\frac{(1-a)(\frac{1}{\text{a1}}+1)}{\text{a1}+1}}\mathrm{\Gamma }(-\frac{a}{\text{a1}+1}+\frac{\text{a1}}{\text{a1}+1}+\frac{2}{\text{a1}+1})J_{\frac{1-a}{\text{a1}+1}}\left(\frac{2\sqrt{b}{\left(x^{\text{a1}}\right)}^{\frac{1}{2}(1+\frac{1}{\text{a1}})}}{(1+\frac{1}{\text{a1}})\text{a1}}\right)\}\right\}$$ ✓ Maple : cpu = 0.799 (sec), leaf count = 71

$$\{y\left(x\right)=x^{-\frac{a}{2}+\frac{1}{2}}({\mathit{Y}}_{\frac{a-1}{\mathit{a}\mathit{1}+1}}\left(2\frac{\sqrt{b}{x}^{\mathit{a}\mathit{1}/2+1/2}}{\mathit{a}\mathit{1}+1}\right)\mathit{\_}\mathit{C}\mathit{2}+{\mathit{J}}_{\frac{a-1}{\mathit{a}\mathit{1}+1}}\left(2\frac{\sqrt{b}{x}^{\mathit{a}\mathit{1}/2+1/2}}{\mathit{a}\mathit{1}+1}\right)\mathit{\_}\mathit{C}\mathit{1})\}$$