2.14   ODE No. 14

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

$$a{x}^m+y^{\prime }(x)+y(x{)}^2=0$$ ✓ Mathematica : cpu = 0.0297844 (sec), leaf count = 254

$$\left\{\{y(x)\to -\frac{i\sqrt{-a}{x}^{\frac{m+2}{2}}(c_1{J}_{\frac{m+1}{m+2}}\left(\frac{2i\sqrt{-a}{x}^{\frac{m}{2}+1}}{m+2}\right)-c_1{J}_{-\frac{m+3}{m+2}}\left(\frac{2i\sqrt{-a}{x}^{\frac{m+2}{2}}}{m+2}\right)-2J_{\frac{1}{m+2}-1}\left(\frac{2i\sqrt{-a}{x}^{\frac{m+2}{2}}}{m+2}\right))-c_1{J}_{-\frac{1}{m+2}}\left(\frac{2i\sqrt{-a}{x}^{\frac{m+2}{2}}}{m+2}\right)}{2x(c_1{J}_{-\frac{1}{m+2}}\left(\frac{2i\sqrt{-a}{x}^{\frac{m+2}{2}}}{m+2}\right)+J_{\frac{1}{m+2}}\left(\frac{2i\sqrt{-a}{x}^{\frac{m+2}{2}}}{m+2}\right))}\}\right\}$$

✓ Maple : cpu = 0.108 (sec), leaf count = 187

$$\{y\left(x\right)=\frac{1}{x}(-\sqrt{a}{x}^{\frac{m}{2}+1}{\mathit{J}}_{\frac{3+m}{m+2}}\left(2\frac{\sqrt{a}{x}^{m/2+1}}{m+2}\right)\mathit{\_}\mathit{C}\mathit{1}-{\mathit{Y}}_{\frac{3+m}{m+2}}\left(2\frac{\sqrt{a}{x}^{m/2+1}}{m+2}\right)\sqrt{a}{x}^{\frac{m}{2}+1}+\mathit{\_}\mathit{C}\mathit{1}{\mathit{J}}_{{(m+2)}^{-1}}\left(2\frac{\sqrt{a}{x}^{m/2+1}}{m+2}\right)+{\mathit{Y}}_{{(m+2)}^{-1}}\left(2\frac{\sqrt{a}{x}^{m/2+1}}{m+2}\right)){(\mathit{\_}\mathit{C}\mathit{1}{\mathit{J}}_{{(m+2)}^{-1}}\left(2\frac{\sqrt{a}{x}^{m/2+1}}{m+2}\right)+{\mathit{Y}}_{{(m+2)}^{-1}}\left(2\frac{\sqrt{a}{x}^{m/2+1}}{m+2}\right))}^{-1}\}$$