2.1149   ODE No. 1149

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

$$y(x)(ax+b)+x^2{y}^{″}(x)=0$$ ✓ Mathematica : cpu = 0.0661289 (sec), leaf count = 212

$$\left\{\{y(x)\to c_2{a}^{\frac{1}{2}(\sqrt{1-4b}+1)-\frac{1}{2}\sqrt{1-4b}}{x}^{\frac{1}{2}(\sqrt{1-4b}+1)-\frac{1}{2}\sqrt{1-4b}}\mathrm{\Gamma }(\sqrt{1-4b}+1)J_{\sqrt{1-4b}}\left(2\sqrt{a}\sqrt{x}\right)+c_1{a}^{\frac{1}{2}(1-\sqrt{1-4b})+\frac{1}{2}\sqrt{1-4b}}{x}^{\frac{1}{2}(1-\sqrt{1-4b})+\frac{1}{2}\sqrt{1-4b}}\mathrm{\Gamma }(1-\sqrt{1-4b})J_{-\sqrt{1-4b}}\left(2\sqrt{a}\sqrt{x}\right)\}\right\}$$

✓ Maple : cpu = 0.015 (sec), leaf count = 47

$$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}\sqrt{x}{\mathit{J}}_{\sqrt{-4b+1}}\left(2\sqrt{a}\sqrt{x}\right)+\mathit{\_}\mathit{C}\mathit{2}\sqrt{x}{\mathit{Y}}_{\sqrt{-4b+1}}\left(2\sqrt{a}\sqrt{x}\right)\}$$