3.99   ODE No. 99

$$\boxed{{\displaystyle x\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+a{\left(y\left(x\right)\right)}^2-by\left(x\right)-c{x}^{\beta }=0}}$$

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

Mathematica: cpu = 0.017002 (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 = 0.078 (sec), leaf count = 237 $$\{y\left(x\right)=-\frac{\mathit{\_}\mathit{C}\mathit{1}}{a}\sqrt{-ac}{x}^{\frac{\beta }{2}}{\mathit{Y}}_{\frac{b+\beta }{\beta }}\left(2\frac{\sqrt{-ac}{x}^{\beta /2}}{\beta }\right){({\mathit{Y}}_{\frac{b}{\beta }}\left(2\frac{\sqrt{-ac}{x}^{\beta /2}}{\beta }\right)\mathit{\_}\mathit{C}\mathit{1}+{\mathit{J}}_{\frac{b}{\beta }}\left(2\frac{\sqrt{-ac}{x}^{\beta /2}}{\beta }\right))}^{-1}-\frac{1}{a}({\mathit{J}}_{\frac{b+\beta }{\beta }}\left(2\frac{\sqrt{-ac}{x}^{\beta /2}}{\beta }\right)\sqrt{-ac}{x}^{\frac{\beta }{2}}-{\mathit{Y}}_{\frac{b}{\beta }}\left(2\frac{\sqrt{-ac}{x}^{\beta /2}}{\beta }\right)\mathit{\_}\mathit{C}\mathit{1}b-b{\mathit{J}}_{\frac{b}{\beta }}\left(2\frac{\sqrt{-ac}{x}^{\beta /2}}{\beta }\right)){({\mathit{Y}}_{\frac{b}{\beta }}\left(2\frac{\sqrt{-ac}{x}^{\beta /2}}{\beta }\right)\mathit{\_}\mathit{C}\mathit{1}+{\mathit{J}}_{\frac{b}{\beta }}\left(2\frac{\sqrt{-ac}{x}^{\beta /2}}{\beta }\right))}^{-1}\}$$