3.24   ODE No. 24

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

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

Mathematica: cpu = 0.011501 (sec), leaf count = 277 $$\left\{\{y(x)\to -\frac{\sqrt{-a}\sqrt{b}{x}^{\frac{\nu +2}{2}}(c_1{J}_{\frac{\nu +1}{\nu +2}}\left(\frac{2\sqrt{-a}\sqrt{b}{x}^{\frac{\nu }{2}+1}}{\nu +2}\right)-c_1{J}_{-\frac{\nu +3}{\nu +2}}\left(\frac{2\sqrt{-a}\sqrt{b}{x}^{\frac{\nu +2}{2}}}{\nu +2}\right)-2J_{\frac{1}{\nu +2}-1}\left(\frac{2\sqrt{-a}\sqrt{b}{x}^{\frac{\nu +2}{2}}}{\nu +2}\right))-c_1{J}_{-\frac{1}{\nu +2}}\left(\frac{2\sqrt{-a}\sqrt{b}{x}^{\frac{\nu +2}{2}}}{\nu +2}\right)}{2ax(c_1{J}_{-\frac{1}{\nu +2}}\left(\frac{2\sqrt{-a}\sqrt{b}{x}^{\frac{\nu +2}{2}}}{\nu +2}\right)+J_{\frac{1}{\nu +2}}\left(\frac{2\sqrt{-a}\sqrt{b}{x}^{\frac{\nu +2}{2}}}{\nu +2}\right))}\}\right\}$$

Maple: cpu = 0.046 (sec), leaf count = 214 $$\{y\left(x\right)=\frac{1}{ax}(-{\mathit{J}}_{\frac{3+\nu }{\nu +2}}\left(2\frac{\sqrt{-ab}{x}^{\nu /2+1}}{\nu +2}\right)\sqrt{-ab}{x}^{\frac{\nu }{2}+1}\mathit{\_}\mathit{C}\mathit{1}-{\mathit{Y}}_{\frac{3+\nu }{\nu +2}}\left(2\frac{\sqrt{-ab}{x}^{\nu /2+1}}{\nu +2}\right)\sqrt{-ab}{x}^{\frac{\nu }{2}+1}+\mathit{\_}\mathit{C}\mathit{1}{\mathit{J}}_{{(\nu +2)}^{-1}}\left(2\frac{\sqrt{-ab}{x}^{\nu /2+1}}{\nu +2}\right)+{\mathit{Y}}_{{(\nu +2)}^{-1}}\left(2\frac{\sqrt{-ab}{x}^{\nu /2+1}}{\nu +2}\right)){(\mathit{\_}\mathit{C}\mathit{1}{\mathit{J}}_{{(\nu +2)}^{-1}}\left(2\frac{\sqrt{-ab}{x}^{\nu /2+1}}{\nu +2}\right)+{\mathit{Y}}_{{(\nu +2)}^{-1}}\left(2\frac{\sqrt{-ab}{x}^{\nu /2+1}}{\nu +2}\right))}^{-1}\}$$

Sage: cpu = 0 (sec), leaf count = 0 $$\text{Maxima was unable to solve this ODE}$$