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 = 0.920893 (sec), leaf count = 485

$$\text{Solve}[c_1=-\frac{\frac{i\sqrt{\frac{2}{\pi }}\sqrt{\frac{1}{2y(x)}+\frac{1}{4}(x+1{)}^2-\frac{1}{4}}(\frac{\sinh \left(\sqrt{\frac{1}{2y(x)}+\frac{1}{4}(x+1{)}^2-\frac{1}{4}}\right)}{\sqrt{\frac{1}{2y(x)}+\frac{1}{4}(x+1{)}^2-\frac{1}{4}}}-\cosh \left(\sqrt{\frac{1}{2y(x)}+\frac{1}{4}(x+1{)}^2-\frac{1}{4}}\right))}{\sqrt{-i\sqrt{\frac{1}{2y(x)}+\frac{1}{4}(x+1{)}^2-\frac{1}{4}}}}-\frac{i\sqrt{\frac{2}{\pi }}(\frac{x+1}{2}+\frac{1}{2})\sinh \left(\sqrt{\frac{1}{2y(x)}+\frac{1}{4}(x+1{)}^2-\frac{1}{4}}\right)}{\sqrt{-i\sqrt{\frac{1}{2y(x)}+\frac{1}{4}(x+1{)}^2-\frac{1}{4}}}}}{\frac{i\sqrt{\frac{2}{\pi }}\sqrt{\frac{1}{2y(x)}+\frac{1}{4}(x+1{)}^2-\frac{1}{4}}(i\sinh \left(\sqrt{\frac{1}{2y(x)}+\frac{1}{4}(x+1{)}^2-\frac{1}{4}}\right)-\frac{i\cosh \left(\sqrt{\frac{1}{2y(x)}+\frac{1}{4}(x+1{)}^2-\frac{1}{4}}\right)}{\sqrt{\frac{1}{2y(x)}+\frac{1}{4}(x+1{)}^2-\frac{1}{4}}})}{\sqrt{-i\sqrt{\frac{1}{2y(x)}+\frac{1}{4}(x+1{)}^2-\frac{1}{4}}}}-\frac{\sqrt{\frac{2}{\pi }}(\frac{x+1}{2}+\frac{1}{2})\cosh \left(\sqrt{\frac{1}{2y(x)}+\frac{1}{4}(x+1{)}^2-\frac{1}{4}}\right)}{\sqrt{-i\sqrt{\frac{1}{2y(x)}+\frac{1}{4}(x+1{)}^2-\frac{1}{4}}}}},y(x)]$$

✓ Maple : cpu = 0.027 (sec), leaf count = 40

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