4.2.29 $y^{\prime }(x)=y(x{)}^2(a{e}^x+y(x))$

ODE
$$y^{\prime }(x)=y(x{)}^2(a{e}^x+y(x))$$ ODE Classification

[_Abel]

Book solution method
Abel ODE, First kind

Mathematica ✓
cpu = 0.876621 (sec), leaf count = 73

$$\text{Solve}[-ia{e}^x=\frac{2e^{-\frac{{(a{e}^{x}y(x)+1)}^2}{2y(x{)}^2}}}{2c_1-i\sqrt{2\pi }\text{erf}\left(\frac{a{e}^{x}y(x)+1}{\sqrt{2}y(x)}\right)},y(x)]$$

Maple ✓
cpu = 0.062 (sec), leaf count = 50

$$\{\mathit{\_}\mathit{C}\mathit{1}+\frac{1}{a{\mathrm{e}}^x}{\mathrm{e}}^{-\frac{{(a{\mathrm{e}}^x+{\left(y\left(x\right)\right)}^{-1})}^2}{2}}+\frac{\sqrt{2}\sqrt{\pi }}{2}\mathit{E}\mathit{r}\mathit{f}\left(\frac{(a{\mathrm{e}}^x+{\left(y\left(x\right)\right)}^{-1})\sqrt{2}}{2}\right)=0\}$$ Mathematica raw input

DSolve[y'[x] == y[x]^2*(a*E^x + y[x]),y[x],x]

Mathematica raw output

Solve[(-I)*a*E^x == 2/(E^((1 + a*E^x*y[x])^2/(2*y[x]^2))*(2*C[1] - I*Sqrt[2*Pi]*
Erf[(1 + a*E^x*y[x])/(Sqrt[2]*y[x])])), y[x]]

Maple raw input

dsolve(diff(y(x),x) = (a*exp(x)+y(x))*y(x)^2, y(x),'implicit')

Maple raw output

_C1+exp(-1/2*(a*exp(x)+1/y(x))^2)/a/exp(x)+1/2*erf(1/2*(a*exp(x)+1/y(x))*2^(1/2)
)*2^(1/2)*Pi^(1/2) = 0