4.3.33 \(y'(x)=e^{y(x)+x}\)

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

\[ \left \{ {{\rm e}^{x}}+{{\rm e}^{-y \relax (x ) }}+{\it \_C1}=0 \right \} \] 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