ODE
\[ y'(x)=e^{y(x)+x} \] ODE Classification
[_separable]
Book solution method
Separable ODE, Neither variable missing
Mathematica ✓
cpu = 0.00883313 (sec), leaf count = 18
\[\left \{\left \{y(x)\to -\log \left (-c_1-e^x\right )\right \}\right \}\]
Maple ✓
cpu = 0.007 (sec), leaf count = 12
\[ \left \{ {{\rm e}^{x}}+{{\rm e}^{-y \left ( x \right ) }}+{\it \_C1}=0 \right \} \] Mathematica raw input
DSolve[y'[x] == E^(x + y[x]),y[x],x]
Mathematica raw output
{{y[x] -> -Log[-E^x - C[1]]}}
Maple raw input
dsolve(diff(y(x),x) = exp(x+y(x)), y(x),'implicit')
Maple raw output
exp(x)+exp(-y(x))+_C1 = 0