3.973   ODE No. 973

$$\boxed{{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)=\frac{y\left(x\right)({\left(y\left(x\right)\right)}^2+y\left(x\right){\mathrm{e}}^{bx}+{\left({\mathrm{e}}^{bx}\right)}^2)}{{\left({\mathrm{e}}^{bx}\right)}^2}=0}}$$

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

Mathematica: cpu = 0.163521 (sec), leaf count = 146 $$\text{Solve}[-\frac{1}{3}(9b-7{)}^{2/3}\text{RootSum}[{\mathrm{\#}\text{1}}^3(9b-7{)}^{2/3}-9\mathrm{\#}\text{1}b+6\mathrm{\#}\text{1}+(9b-7{)}^{2/3}\mathrm{\&},\frac{\log (\frac{3e^{-2bx}y(x)+e^{-bx}}{\sqrt[3]{(9b-7)e^{-3bx}}}-\mathrm{\#}\text{1})}{{\mathrm{\#}\text{1}}^2(-(9b-7{)}^{2/3})+3b-2}\mathrm{\&}]=\frac{1}{9}x{e}^{2bx}{((9b-7)e^{-3bx})}^{2/3}+c_1,y(x)]$$

Maple: cpu = 0.234 (sec), leaf count = 136 $$\{y\left(x\right)=\frac{1}{2}\tan \left(\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-2\mathit{\_}\mathit{Z}{\mathrm{e}}^{bx}-\ln (-(4{(\tan \left(\mathit{\_}\mathit{Z}\right))}^{2}b-3{(\tan \left(\mathit{\_}\mathit{Z}\right))}^2+4b-3){(-\tan \left(\mathit{\_}\mathit{Z}\right)\sqrt{-{\left({\mathrm{e}}^{bx}\right)}^2(4b-3)}+{\mathrm{e}}^{bx})}^{-2})\sqrt{-{\left({\mathrm{e}}^{bx}\right)}^2(4b-3)}+\mathit{\_}\mathit{C}\mathit{1}\sqrt{-{\left({\mathrm{e}}^{bx}\right)}^2(4b-3)}-2x\sqrt{-{\left({\mathrm{e}}^{bx}\right)}^2(4b-3)})\right)\sqrt{-{\mathrm{e}}^{2bx}(4b-3)}-\frac{{\mathrm{e}}^{bx}}{2}\}$$