ODE
\[ (2 x+1) y'(x)=4 e^{-y(x)}-2 \] ODE Classification
[_separable]
Book solution method
Separable ODE, Neither variable missing
Mathematica ✓
cpu = 0.380621 (sec), leaf count = 21
\[\left \{\left \{y(x)\to \log \left (2-\frac {e^{c_1}}{2 x+1}\right )\right \}\right \}\]
Maple ✓
cpu = 0.2 (sec), leaf count = 34
\[\left [y \left (x \right ) = -\ln \left (\frac {1+2 x}{-1+4 x \,{\mathrm e}^{2 \textit {\_C1}}+2 \,{\mathrm e}^{2 \textit {\_C1}}}\right )-2 \textit {\_C1}\right ]\] Mathematica raw input
DSolve[(1 + 2*x)*y'[x] == -2 + 4/E^y[x],y[x],x]
Mathematica raw output
{{y[x] -> Log[2 - E^C[1]/(1 + 2*x)]}}
Maple raw input
dsolve((1+2*x)*diff(y(x),x) = 4*exp(-y(x))-2, y(x))
Maple raw output
[y(x) = -ln((1+2*x)/(-1+4*x*exp(2*_C1)+2*exp(2*_C1)))-2*_C1]