2.622   ODE No. 622

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

$$y^{\prime }(x)=\frac{1}{y(x)+\sqrt{3x+1}+2}$$ ✓ Mathematica : cpu = 0.229631 (sec), leaf count = 140

$$\text{Solve}[6\sqrt{33}{\tanh }^{-1}\left(\frac{3y(x)+7\sqrt{3x+1}+6}{\sqrt{33}(y(x)+\sqrt{3x+1}+2)}\right)+44c_1=33(\log \left(\frac{-3\sqrt{3x+1}y(x{)}^2-3(3x+4\sqrt{3x+1}+1)y(x)+6x(\sqrt{3x+1}-3)-10\sqrt{3x+1}-6}{2(3x+1{)}^{3/2}}\right)+\log (12x+4)),y(x)]$$ ✓ Maple : cpu = 0.443 (sec), leaf count = 77

$$\{\ln ((3y\left(x\right)+6)\sqrt{3x+1}+3{\left(y\left(x\right)\right)}^2-6x+12y\left(x\right)+10)-6\frac{\sqrt{3x+1}}{\sqrt{99x+33}}\mathit{A}\mathit{r}\mathit{t}\mathit{a}\mathit{n}\mathit{h}\left(\frac{3\sqrt{3x+1}+6y\left(x\right)+12}{\sqrt{99x+33}}\right)-\mathit{\_}\mathit{C}\mathit{1}=0\}$$