2.99   ODE No. 99

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

$$ay(x{)}^2-by(x)-c{x}^{\beta }+x{y}^{\prime }(x)=0$$ ✓ Mathematica : cpu = 0.155888 (sec), leaf count = 244

$$\left\{\{y(x)\to -\frac{\sqrt{-a}\sqrt{c}{x}^{\beta /2}(-2J_{\frac{b}{\beta }-1}\left(\frac{2\sqrt{-a}\sqrt{c}{x}^{\beta /2}}{\beta }\right)+c_1{J}_{1-\frac{b}{\beta }}\left(\frac{2\sqrt{-a}\sqrt{c}{x}^{\beta /2}}{\beta }\right)-c_1{J}_{-\frac{b+\beta }{\beta }}\left(\frac{2\sqrt{-a}\sqrt{c}{x}^{\beta /2}}{\beta }\right))-b{c}_1{J}_{-\frac{b}{\beta }}\left(\frac{2\sqrt{-a}\sqrt{c}{x}^{\beta /2}}{\beta }\right)}{2a(J_{\frac{b}{\beta }}\left(\frac{2\sqrt{-a}\sqrt{c}{x}^{\beta /2}}{\beta }\right)+c_1{J}_{-\frac{b}{\beta }}\left(\frac{2\sqrt{-a}\sqrt{c}{x}^{\beta /2}}{\beta }\right))}\}\right\}$$ ✓ Maple : cpu = 0.091 (sec), leaf count = 171

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