3.204   ODE No. 204

$$\boxed{{\displaystyle y\left(x\right)\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+ay\left(x\right)+x=0}}$$

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

Mathematica: cpu = 0.096512 (sec), leaf count = 70 $$\text{Solve}[\frac{1}{2}\log (\frac{ay(x)}{x}+\frac{y(x{)}^2}{x^2}+1)-\frac{a{\tan }^{-1}\left(\frac{a+\frac{2y(x)}{x}}{\sqrt{4-a^2}}\right)}{\sqrt{4-a^2}}=c_1-\log (x),y(x)]$$

Maple: cpu = 0.218 (sec), leaf count = 88 $$\{y\left(x\right)=\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}({\mathit{\_}\mathit{Z}}^2-{\mathrm{e}}^{\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}\left(x^2({(\tanh \left(\frac{2\mathit{\_}\mathit{C}\mathit{1}+\mathit{\_}\mathit{Z}+2\ln \left(x\right)}{2a}\sqrt{a^2-4}\right))}^2{a}^2-4{(\tanh \left(1/2\frac{\sqrt{a^2-4}(2\mathit{\_}\mathit{C}\mathit{1}+\mathit{\_}\mathit{Z}+2\ln \left(x\right))}{a}\right))}^2-a^2-4{\mathrm{e}}^{\mathit{\_}\mathit{Z}}+4)\right)}+1+\mathit{\_}\mathit{Z}a)x\}$$