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 = 0.341989 (sec), leaf count = 41
\[\text {Solve}\left [\left \{\log (1-K[1])+x=\log (K[1])+\log (K[1]+1)+c_1,K[1]=\log \left (K[1]^2-1\right )+y(x)\right \},\{y(x),K[1]\}\right ]\]
Maple ✓
cpu = 0.086 (sec), leaf count = 31
\[\left [x -\left (\int _{}^{y \left (x \right )}\frac {1}{\RootOf \left (-{\mathrm e}^{-\textit {\_a} +\textit {\_Z}}+\textit {\_Z}^{2}-1\right )}d \textit {\_a} \right )-\textit {\_C1} = 0\right ]\] 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[1]] == C[1] + Log[K[1]] + Log[1 + K[1]], K[1] == Log[-1 + K[1]^2] + y[x]}, {y[x], K[1]}]
Maple raw input
dsolve(exp(diff(y(x),x)-y(x))-diff(y(x),x)^2+1 = 0, y(x))
Maple raw output
[x-Intat(1/RootOf(-exp(-_a+_Z)+_Z^2-1),_a = y(x))-_C1 = 0]