2.41   ODE No. 41

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

$$axy(x{)}^3+by(x{)}^2+y^{\prime }(x)=0$$ ✓ Mathematica : cpu = 0.0773069 (sec), leaf count = 103

$$\text{Solve}[-\frac{b^2(\frac{2{\tan }^{-1}\left(\frac{-2axy(x)-b}{b\sqrt{-\frac{4a}{b^2}-1}}\right)}{\sqrt{-\frac{4a}{b^2}-1}}-\log \left(\frac{a(-x)y(x)(-axy(x)-b)-a}{a^2{x}^{2}y(x{)}^2}\right))}{2a}=c_1-\frac{b^2\log (x)}{a},y(x)]$$

✓ Maple : cpu = 0.214 (sec), leaf count = 103

$$\{y\left(x\right)=\frac{1}{x}{\mathrm{e}}^{\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(2\sqrt{b^2+4a}b\mathit{A}\mathit{r}\mathit{t}\mathit{a}\mathit{n}\mathit{h}\left(\frac{2a{\mathrm{e}}^{\mathit{\_}\mathit{Z}}+b}{\sqrt{b^2+4a}}\right)-\ln \left(x^2(a{\mathrm{e}}^{2\mathit{\_}\mathit{Z}}+b{\mathrm{e}}^{\mathit{\_}\mathit{Z}}-1)\right)b^2+2\mathit{\_}\mathit{C}\mathit{1}{b}^2+2\mathit{\_}\mathit{Z}{b}^2-4\ln \left(x^2(a{\mathrm{e}}^{2\mathit{\_}\mathit{Z}}+b{\mathrm{e}}^{\mathit{\_}\mathit{Z}}-1)\right)a+8\mathit{\_}\mathit{C}\mathit{1}a+8\mathit{\_}\mathit{Z}a)}\}$$