ODE
\[ (2 x+1) y'(x)=4 e^{-y(x)}-2 \] ODE Classification
[_separable]
Book solution method
Separable ODE, Neither variable missing
Mathematica ✓
cpu = 0.015125 (sec), leaf count = 20
\[\left \{\left \{y(x)\to \log \left (\frac {e^{c_1}}{2 x+1}+2\right )\right \}\right \}\]
Maple ✓
cpu = 0.02 (sec), leaf count = 29
\[ \left \{ {\it \_C1}+\ln \left ( 1+2\,x \right ) +\ln \left ( 2\,{{\rm e}^{-y \left ( x \right ) }}-1 \right ) -\ln \left ( {{\rm e}^{-y \left ( x \right ) }} \right ) =0 \right \} \] 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),'implicit')
Maple raw output
_C1+ln(1+2*x)+ln(2*exp(-y(x))-1)-ln(exp(-y(x))) = 0