ODE
\[ y'(x)=e^x \left (a+b e^{-y(x)}\right ) \] ODE Classification
[_separable]
Book solution method
Separable ODE, Neither variable missing
Mathematica ✓
cpu = 0.403331 (sec), leaf count = 24
\[\left \{\left \{y(x)\to \log \left (\frac {-b+e^{a \left (e^x+c_1\right )}}{a}\right )\right \}\right \}\]
Maple ✓
cpu = 0.19 (sec), leaf count = 24
\[\left [y \left (x \right ) = -\ln \left (\frac {a}{{\mathrm e}^{a \,{\mathrm e}^{x}+\textit {\_C1} a}-b}\right )\right ]\] Mathematica raw input
DSolve[y'[x] == E^x*(a + b/E^y[x]),y[x],x]
Mathematica raw output
{{y[x] -> Log[(-b + E^(a*(E^x + C[1])))/a]}}
Maple raw input
dsolve(diff(y(x),x) = exp(x)*(a+b*exp(-y(x))), y(x))
Maple raw output
[y(x) = -ln(a/(exp(a*exp(x)+_C1*a)-b))]