2.978   ODE No. 978

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

$$y^{\prime }(x)=\frac{y(x)(x^2+xy(x)+y(x{)}^2+x)}{x^2}$$ ✓ Mathematica : cpu = 0.142509 (sec), leaf count = 60

$$\text{Solve}[-\frac{1}{2}\log (\frac{y(x{)}^2}{x^2}+\frac{y(x)}{x}+1)+\log \left(\frac{y(x)}{x}\right)-\frac{{\tan }^{-1}\left(\frac{\frac{2y(x)}{x}+1}{\sqrt{3}}\right)}{\sqrt{3}}=x+c_1,y(x)]$$ ✓ Maple : cpu = 0.887 (sec), leaf count = 71

$$\{y\left(x\right)=\frac{\sqrt{3}x}{2}\tan \left(\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-\sqrt{3}\ln \left(3\right)-\sqrt{3}\ln \left(\frac{4}{3+3{(\tan \left(\mathit{\_}\mathit{Z}\right))}^2}\right)-2\sqrt{3}\ln (-1/6\sqrt{3}+1/2\tan \left(\mathit{\_}\mathit{Z}\right))+2\sqrt{3}\mathit{\_}\mathit{C}\mathit{1}+2\sqrt{3}x+2\mathit{\_}\mathit{Z})\right)-\frac{x}{2}\}$$