\[ -\left (y'(x)-1\right )^2+e^{-2 x} y'(x)^2+e^{-2 y(x)}=0 \] ✓ Mathematica : cpu = 3.27401 (sec), leaf count = 241
\[\left \{\left \{y(x)\to \log \left (-\frac {i e^{-c_1} \left (e^x+1\right ) \left (e^{2 c_1+x}-e^{2 c_1}+e^x+1\right )}{2 \sqrt {\left (e^x+1\right )^2}}\right )\right \},\left \{y(x)\to \log \left (\frac {i e^{-c_1} \left (e^x+1\right ) \left (e^{2 c_1+x}-e^{2 c_1}+e^x+1\right )}{2 \sqrt {\left (e^x+1\right )^2}}\right )\right \},\text {Solve}\left [2 c_1+\log \left (1-e^{2 y(x)}\right )+2 x+\log \left (1-e^x\right )+\log \left (e^x-1\right )=\log \left (\sqrt {e^{2 (y(x)+x)} \left (e^{2 y(x)}+e^{2 x}-1\right )}+e^{2 y(x)+x}-e^x-e^{2 x}\right )+\log \left (\sqrt {e^{2 (y(x)+x)} \left (e^{2 y(x)}+e^{2 x}-1\right )}+e^{2 y(x)+x}-e^x+e^{2 x}\right ),y(x)\right ]\right \}\]
✓ Maple : cpu = 0.711 (sec), leaf count = 65
\[ \left \{ y \left ( x \right ) =x+\ln \left ( {\frac {1}{{{\rm e}^{x}}} \left ( -1-\sqrt { \left ( {{\rm e}^{x}} \right ) ^{2}-{\frac { \left ( {{\rm e}^{x}} \right ) ^{2}}{ \left ( {{\rm e}^{{\it \_C1}}} \right ) ^{2}}}} \right ) } \right ) +{\it \_C1},y \left ( x \right ) =x+\ln \left ( {\frac {1}{{{\rm e}^{x}}} \left ( -1+\sqrt { \left ( {{\rm e}^{x}} \right ) ^{2}-{\frac { \left ( {{\rm e}^{x}} \right ) ^{2}}{ \left ( {{\rm e}^{{\it \_C1}}} \right ) ^{2}}}} \right ) } \right ) +{\it \_C1} \right \} \]