2.973   ODE No. 973

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

$$y^{\prime }(x)=e^{-2bx}y(x)(e^{bx}y(x)+e^{2bx}+y(x{)}^2)$$ ✓ Mathematica : cpu = 0.1731 (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 = 0.338 (sec), leaf count = 135

$$\{y\left(x\right)=-\frac{1}{2}\tan \left(\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-\ln \left((4{(\tan \left(\mathit{\_}\mathit{Z}\right))}^{2}b-3{(\tan \left(\mathit{\_}\mathit{Z}\right))}^2+4b-3){(\tan \left(\mathit{\_}\mathit{Z}\right)\sqrt{-{\left({\mathrm{e}}^{bx}\right)}^2(4b-3)}+{\mathrm{e}}^{bx})}^{-2}\right)\sqrt{-{\left({\mathrm{e}}^{bx}\right)}^2(4b-3)}+\mathit{\_}\mathit{C}\mathit{1}\sqrt{-{\left({\mathrm{e}}^{bx}\right)}^2(4b-3)}-2x\sqrt{-{\left({\mathrm{e}}^{bx}\right)}^2(4b-3)}+2\mathit{\_}\mathit{Z}{\mathrm{e}}^{bx})\right)\sqrt{-{\left({\mathrm{e}}^{bx}\right)}^2(4b-3)}-\frac{{\mathrm{e}}^{bx}}{2}\}$$