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 = 0.281619 (sec), leaf count = 18

\[\left \{\left \{y(x)\to -\log \left (-e^x-c_1\right )\right \}\right \}\]

Maple ✓
cpu = 0.022 (sec), leaf count = 13

\[\left [y \left (x \right ) = \ln \left (-\frac {1}{{\mathrm e}^{x}+\textit {\_C1}}\right )\right ]\] 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))

Maple raw output

[y(x) = ln(-1/(exp(x)+_C1))]