\[ y'(x)^2-2 y'(x)-y(x)^2=0 \] ✓ Mathematica : cpu = 0.077079 (sec), leaf count = 73
DSolve[-y[x]^2 - 2*Derivative[1][y][x] + Derivative[1][y][x]^2 == 0,y[x],x]
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [-\frac {\sqrt {\text {$\#$1}^2+1}}{\text {$\#$1}}-\frac {1}{\text {$\#$1}}+\sinh ^{-1}(\text {$\#$1})\& \right ][-x+c_1]\right \},\left \{y(x)\to \text {InverseFunction}\left [-\frac {\sqrt {\text {$\#$1}^2+1}}{\text {$\#$1}}+\frac {1}{\text {$\#$1}}+\sinh ^{-1}(\text {$\#$1})\& \right ][x+c_1]\right \}\right \}\] ✓ Maple : cpu = 0.033 (sec), leaf count = 85
dsolve(diff(y(x),x)^2-2*diff(y(x),x)-y(x)^2 = 0,y(x))
\[x -\frac {1}{y \left (x \right )}-\frac {\left (y \left (x \right )^{2}+1\right )^{\frac {3}{2}}}{y \left (x \right )}+y \left (x \right ) \sqrt {y \left (x \right )^{2}+1}+\arcsinh \left (y \left (x \right )\right )-c_{1} = 0\]