2.42   ODE No. 42

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

$$y^{\prime }(x)-x(x+2)y(x{)}^3-(x+3)y(x{)}^2=0$$ ✓ Mathematica : cpu = 1.78985 (sec), leaf count = 136

$$\text{Solve}[c_1=-\frac{i(x\sinh \left(\frac{1}{2}\sqrt{\frac{2}{y(x)}+x(x+2)}\right)+\sqrt{\frac{2}{y(x)}+x(x+2)}\cosh \left(\frac{1}{2}\sqrt{\frac{2}{y(x)}+x(x+2)}\right))}{\sqrt{\frac{2}{y(x)}+x(x+2)}\sinh \left(\frac{1}{2}\sqrt{\frac{2}{y(x)}+x(x+2)}\right)+x\cosh \left(\frac{1}{2}\sqrt{\frac{2}{y(x)}+x(x+2)}\right)},y(x)]$$

✓ Maple : cpu = 0.044 (sec), leaf count = 40

$$\{\mathit{\_}\mathit{C}\mathit{1}+\mathit{A}\mathit{r}\mathit{t}\mathit{a}\mathit{n}\mathit{h}\left(x\sqrt{y\left(x\right)}\frac{1}{\sqrt{x(x+2)y\left(x\right)+2}}\right)+\frac{1}{2}\sqrt{x(x+2)y\left(x\right)+2}\frac{1}{\sqrt{y\left(x\right)}}=0\}$$