\[ -\left (y'(x)-1\right )^2+e^{-2 x} y'(x)^2+e^{-2 y(x)}=0 \] ✓ Mathematica : cpu = 12.1587 (sec), leaf count = 545
DSolve[E^(-2*y[x]) - (-1 + Derivative[1][y][x])^2 + Derivative[1][y][x]^2/E^(2*x) == 0,y[x],x]
\[\left \{\text {Solve}\left [-\frac {\left (e^{2 \text {arctanh}\left (1-2 e^x\right )+x}+e^x-1\right ) \sqrt {e^{2 y(x)}+e^{2 x}-1} e^{y(x)-2 \text {arctanh}\left (1-2 e^x\right )} \log \left (\sqrt {e^{2 y(x)}+e^{2 x}-1}+e^{y(x)}\right )}{\sqrt {e^{2 (y(x)+x)} \left (e^{2 y(x)}+e^{2 x}-1\right )}}-y(x)+\log \left (e^{y(x)}\right )-\frac {1}{2} \log \left (e^{y(x)}-1\right )-\frac {1}{2} \log \left (e^{y(x)}+1\right )+\frac {1}{2} \log \left (\sqrt {e^{2 y(x)+2 x} \left (e^{2 y(x)}+e^{2 x}-1\right )}+e^{2 y(x)+x}-e^x-e^{2 x}\right )+\frac {1}{2} \log \left (\sqrt {e^{2 y(x)+2 x} \left (e^{2 y(x)}+e^{2 x}-1\right )}+e^{2 y(x)+x}-e^x+e^{2 x}\right )-x-\frac {1}{2} \log \left (1-e^x\right )-\frac {1}{2} \log \left (e^x-1\right )=c_1,y(x)\right ],\text {Solve}\left [\frac {\left (e^{2 \text {arctanh}\left (1-2 e^x\right )+x}+e^x-1\right ) \sqrt {e^{2 y(x)}+e^{2 x}-1} e^{y(x)-2 \text {arctanh}\left (1-2 e^x\right )} \log \left (\sqrt {e^{2 y(x)}+e^{2 x}-1}+e^{y(x)}\right )}{\sqrt {e^{2 (y(x)+x)} \left (e^{2 y(x)}+e^{2 x}-1\right )}}-\frac {1}{2} \log \left (\sqrt {e^{2 y(x)+2 x} \left (e^{2 y(x)}+e^{2 x}-1\right )}+e^{2 y(x)+x}-e^x-e^{2 x}\right )-\frac {1}{2} \log \left (\sqrt {e^{2 y(x)+2 x} \left (e^{2 y(x)}+e^{2 x}-1\right )}+e^{2 y(x)+x}-e^x+e^{2 x}\right )+\frac {1}{2} \left (2 y(x)-2 \log \left (e^{y(x)}\right )+\log \left (e^{y(x)}-1\right )+\log \left (e^{y(x)}+1\right )\right )+x-\frac {1}{2} \log \left (1-e^x\right )+\frac {1}{2} \log \left (e^x-1\right )+\log \left (e^x+1\right )=c_1,y(x)\right ]\right \}\] ✓ Maple : cpu = 0.493 (sec), leaf count = 113
dsolve(exp(-2*x)*diff(y(x),x)^2-(diff(y(x),x)-1)^2+exp(-2*y(x)) = 0,y(x))
\[y \left (x \right ) = c_{1}-\ln \left (\frac {{\mathrm e}^{-2 x} {\mathrm e}^{2 c_{1}}-\sqrt {\left ({\mathrm e}^{4 c_{1}}-{\mathrm e}^{2 c_{1}}\right ) {\mathrm e}^{-2 x}}}{-{\mathrm e}^{-2 x} {\mathrm e}^{2 c_{1}}+{\mathrm e}^{2 c_{1}}-1}\right )\]