3.14   ODE No. 14

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

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

Mathematica: cpu = 0.010501 (sec), leaf count = 254$$y(x)=-\frac{i\sqrt{-a}{x}^{\frac{m+2}{2}}(c_1{J}_{\frac{m+1}{m+2}}(z)-c_1{J}_{-\frac{m+3}{m+2}}(z)-2J_{\frac{1}{m+2}-1}(z))-c_1{J}_{-\frac{1}{m+2}}(z)}{2x(c_1{J}_{-\frac{1}{m+2}}(z)+J_{\frac{1}{m+2}}(z))}$$ Where $$z=\left(\frac{2i\sqrt{-a}{x}^{\frac{m}{2}+1}}{m+2}\right)$$

Maple: cpu = 0.093 (sec), leaf count = 189 $$\{y\left(x\right)=-\frac{1}{x}(\sqrt{a}{x}^{\frac{m}{2}+1}{\mathit{J}}_{\frac{3+m}{m+2}}\left(2\frac{\sqrt{a}{x}^{m/2+1}}{m+2}\right)\mathit{\_}\mathit{C}\mathit{1}+{\mathit{Y}}_{\frac{3+m}{m+2}}\left(2\frac{\sqrt{a}{x}^{m/2+1}}{m+2}\right)\sqrt{a}{x}^{\frac{m}{2}+1}-\mathit{\_}\mathit{C}\mathit{1}{\mathit{J}}_{{(m+2)}^{-1}}\left(2\frac{\sqrt{a}{x}^{m/2+1}}{m+2}\right)-{\mathit{Y}}_{{(m+2)}^{-1}}\left(2\frac{\sqrt{a}{x}^{m/2+1}}{m+2}\right)){(\mathit{\_}\mathit{C}\mathit{1}{\mathit{J}}_{{(m+2)}^{-1}}\left(2\frac{\sqrt{a}{x}^{m/2+1}}{m+2}\right)+{\mathit{Y}}_{{(m+2)}^{-1}}\left(2\frac{\sqrt{a}{x}^{m/2+1}}{m+2}\right))}^{-1}\}$$

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