ODE
\[ -y'(x)^2+e^{y'(x)-y(x)}+1=0 \] ODE Classification
[_quadrature]
Book solution method
Missing Variables ODE, Independent variable missing, Solve for \(y\)
Mathematica ✓
cpu = 0.112294 (sec), leaf count = 35
\[\text {Solve}\left [\left \{\log (1-\text {K$\$$263323})+x=c_1+\log (\text {K$\$$263323})+\log (\text {K$\$$263323}+1),\text {K$\$$263323}=\log \left (\text {K$\$$263323}^2-1\right )+y(x)\right \},\{y(x),\text {K$\$$263323}\}\right ]\]
Maple ✓
cpu = 0.03 (sec), leaf count = 31
\[ \left \{ x-\int ^{y \left ( x \right ) }\! \left ( {\it RootOf} \left ( -{{\rm e}^{-{\it \_a}+{\it \_Z}}}+{{\it \_Z}}^{2}-1 \right ) \right ) ^{-1}{d{\it \_a}}-{\it \_C1}=0 \right \} \] 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$263323 == 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