\[ \boxed { \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}-2\,y \left ( x \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -2\,x=0} \]
Mathematica: cpu = 0.670085 (sec), leaf count = 53 \[ \text {Solve}\left [\left \{x=\frac {c_1 \text {K$\$$1205645}}{\sqrt {\text {K$\$$1205645}^2+1}}+\frac {\text {K$\$$1205645} \sinh ^{-1}(\text {K$\$$1205645})}{2 \sqrt {\text {K$\$$1205645}^2+1}},y(x)=\frac {\text {K$\$$1205645}}{2}-\frac {x}{\text {K$\$$1205645}}\right \},\{y(x),\text {K$\$$1205645}\}\right ] \]
Maple: cpu = 0.499 (sec), leaf count = 217 \[ \left \{ {{\it \_C1} \left ( -2\,y \left ( x \right ) +2\,\sqrt { \left ( y \left ( x \right ) \right ) ^{2}+2\,x} \right ) {\frac {1}{\sqrt {2\, \left ( y \left ( x \right ) \right ) ^{2}+2\,x-2\,y \left ( x \right ) \sqrt { \left ( y \left ( x \right ) \right ) ^{2}+2\,x}+1}}}}+x-{\frac { 1}{2} \left ( -y \left ( x \right ) +\sqrt { \left ( y \left ( x \right ) \right ) ^{2}+2\,x} \right ) {\it Arcsinh} \left ( -y \left ( x \right ) + \sqrt { \left ( y \left ( x \right ) \right ) ^{2}+2\,x} \right ) {\frac { 1}{\sqrt {2\, \left ( y \left ( x \right ) \right ) ^{2}+2\,x-2\,y \left ( x \right ) \sqrt { \left ( y \left ( x \right ) \right ) ^{2}+2\,x }+1}}}}=0,{{\it \_C1} \left ( 2\,y \left ( x \right ) +2\,\sqrt { \left ( y \left ( x \right ) \right ) ^{2}+2\,x} \right ) {\frac {1}{\sqrt {2\, \left ( y \left ( x \right ) \right ) ^{2}+2\,x+2\,y \left ( x \right ) \sqrt { \left ( y \left ( x \right ) \right ) ^{2}+2\,x}+1}}}}+x-{\frac { 1}{2} \left ( y \left ( x \right ) +\sqrt { \left ( y \left ( x \right ) \right ) ^{2}+2\,x} \right ) {\it Arcsinh} \left ( y \left ( x \right ) + \sqrt { \left ( y \left ( x \right ) \right ) ^{2}+2\,x} \right ) {\frac { 1}{\sqrt {2\, \left ( y \left ( x \right ) \right ) ^{2}+2\,x+2\,y \left ( x \right ) \sqrt { \left ( y \left ( x \right ) \right ) ^{2}+2\,x }+1}}}}=0 \right \} \]