4.23.50 $-y^{\prime }(x{)}^2+e^{y^{\prime }(x)-y(x)}+1=0$

ODE
$$-y^{\prime }(x{)}^2+e^{y^{\prime }(x)-y(x)}+1=0$$ ODE Classification

[_quadrature]

Book solution method
Missing Variables ODE, Independent variable missing, Solve for $y$

Mathematica ✓
cpu = 0.112294 (sec), leaf count = 35

$$\text{Solve}[\{\log (1-\text{K}\mathrm{\$}\text{263323})+x=c_1+\log (\text{K}\mathrm{\$}\text{263323})+\log (\text{K}\mathrm{\$}\text{263323}+1),\text{K}\mathrm{\$}\text{263323}=\log ({\text{K}\mathrm{\$}\text{263323}}^2-1)+y(x)\},\{y(x),\text{K}\mathrm{\$}\text{263323}\}]$$

Maple ✓
cpu = 0.03 (sec), leaf count = 31

$$\{x-{\int }^{y\left(x\right)}{\left(\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-{\mathrm{e}}^{-\mathit{\_}\mathit{a}+\mathit{\_}\mathit{Z}}+{\mathit{\_}\mathit{Z}}^2-1)\right)}^{-1}d\mathit{\_}\mathit{a}-\mathit{\_}\mathit{C}\mathit{1}=0\}$$ Mathematica raw input

DSolve[1 + E^(-y[x] + y'[x]) - y'[x]^2 == 0,y[x],x]

Mathematica raw output

Solve[{x + Log[1 - K$263323] == C[1] + Log[K$263323] + Log[1 + K$263323], K$2633
23 == Log[-1 + K$263323^2] + y[x]}, {y[x], K$263323}]

Maple raw input

dsolve(exp(diff(y(x),x)-y(x))-diff(y(x),x)^2+1 = 0, y(x),'implicit')

Maple raw output

x-Intat(1/RootOf(-exp(-_a+_Z)+_Z^2-1),_a = y(x))-_C1 = 0