2.580   ODE No. 580

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

$$y^{\prime }(x)=e^{bx}F(e^{-bx}y(x))$$ ✓ Mathematica : cpu = 24.8231 (sec), leaf count = 200

$$\text{Solve}[{\int }_1^{y(x)}(\frac{1}{bK[2]-e^{bx}F(e^{-bx}K[2])}-{\int }_1^x(\frac{F^{\prime }(K[2]e^{-bK[1]})}{e^{bK[1]}F(K[2]e^{-bK[1]})-bK[2]}-\frac{e^{bK[1]}F(K[2]e^{-bK[1]})(F^{\prime }(K[2]e^{-bK[1]})-b)}{{(e^{bK[1]}F(K[2]e^{-bK[1]})-bK[2])}^2})dK[1])dK[2]+{\int }_1^x\frac{e^{bK[1]}F(y(x)e^{-bK[1]})}{e^{bK[1]}F(y(x)e^{-bK[1]})-by(x)}dK[1]=c_1,y(x)]$$

✓ Maple : cpu = 0.062 (sec), leaf count = 31

$$\{y\left(x\right)=\frac{\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-x+{\int }^{\mathit{\_}\mathit{Z}}{(F\left(\mathit{\_}\mathit{a}\right)-\mathit{\_}\mathit{a}b)}^{-1}d\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1})}{{\mathrm{e}}^{-bx}}\}$$