4.21.45 $y^{\prime }(x{)}^3+(e^{2x}+e^{3x})e^{-2y(x)}{y}^{\prime }(x)-e^{3x-2y(x)}=0$

ODE
$$y^{\prime }(x{)}^3+(e^{2x}+e^{3x})e^{-2y(x)}{y}^{\prime }(x)-e^{3x-2y(x)}=0$$ ODE Classification

[`y=_G(x,y')`]

Book solution method
Change of variable

Mathematica ✗
cpu = 600.047 (sec), leaf count = 0 , timed out

$Aborted

Maple ✓
cpu = 0.994 (sec), leaf count = 42

$$\{[y\left(\mathit{\_}\mathit{T}\right)=-\ln (\mathit{\_}\mathit{T}-1)+\ln \left(\mathit{\_}\mathit{T}\right)+\mathit{\_}\mathit{C}\mathit{1}-\frac{1}{2}\ln (-\frac{{\mathit{\_}\mathit{T}}^2}{{\mathrm{e}}^{\mathit{\_}\mathit{C}\mathit{1}}+1}),x\left(\mathit{\_}\mathit{T}\right)=-\ln (\mathit{\_}\mathit{T}-1)+\ln \left(\mathit{\_}\mathit{T}\right)+\mathit{\_}\mathit{C}\mathit{1}]\}$$ Mathematica raw input

DSolve[-E^(3*x - 2*y[x]) + ((E^(2*x) + E^(3*x))*y'[x])/E^(2*y[x]) + y'[x]^3 == 0,y[x],x]

Mathematica raw output

$Aborted

Maple raw input

dsolve(diff(y(x),x)^3+exp(-2*y(x))*(exp(2*x)+exp(3*x))*diff(y(x),x)-exp(3*x-2*y(x)) = 0, y(x),'implicit')

Maple raw output

[y(_T) = -ln(_T-1)+ln(_T)+_C1-1/2*ln(-_T^2/(exp(_C1)+1)), x(_T) = -ln(_T-1)+ln(_
T)+_C1]