4.5.46 \((2 x+1) y'(x)=4 e^{-y(x)}-2\)

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

\[ \left \{ {\it \_C1}+\ln \left (1+2\,x \right ) +\ln \left (2\,{{\rm e}^{-y \relax (x ) }}-1 \right ) -\ln \left ({{\rm e}^{-y \relax (x ) }} \right ) =0 \right \} \] 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