2.1155   ODE No. 1155

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

$$y(x)(a{x}^k-(b-1)b)+x^2{y}^{″}(x)=0$$ ✓ Mathematica : cpu = 0.0617713 (sec), leaf count = 116

$$\left\{\{y(x)\to k^{-1/k}{a}^{\frac{1}{2}/k}{\left(x^k\right)}^{\frac{1}{2}/k}(c_1\mathrm{\Gamma }\left(\frac{-2b+k+1}{k}\right)J_{\frac{1-2b}{k}}\left(\frac{2\sqrt{a}\sqrt{x^k}}{k}\right)+c_2\mathrm{\Gamma }\left(\frac{2b+k-1}{k}\right)J_{\frac{2b-1}{k}}\left(\frac{2\sqrt{a}\sqrt{x^k}}{k}\right))\}\right\}$$

✓ Maple : cpu = 0.052 (sec), leaf count = 67

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