\[ \boxed { x \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}-2\,{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -y \left ( x \right ) =0} \]
Mathematica: cpu = 30.779909 (sec), leaf count = 66 \[ \text {Solve}\left [\left \{x=\frac {y(\text {K$\$$1211643})+2 \text {K$\$$1211643}}{\text {K$\$$1211643}^2},y(x)=c_1 e^{2 (\log (\text {K$\$$1211643})-\log (1-\text {K$\$$1211643}))}+e^{2 (\log (\text {K$\$$1211643})-\log (1-\text {K$\$$1211643}))} \left (-\frac {2}{\text {K$\$$1211643}}-2 \log (\text {K$\$$1211643})\right )\right \},\{y(x),\text {K$\$$1211643}\}\right ] \]
Maple: cpu = 0.468 (sec), leaf count = 63 \[ \left \{ y \left ( x \right ) =x{{\rm e}^{2\,{\it RootOf} \left ( -x{ {\rm e}^{2\,{\it \_Z}}}+2\,x{{\rm e}^{{\it \_Z}}}+2\,{{\rm e}^{{\it \_Z}}}+{\it \_C1}-2\,{\it \_Z}-x \right ) }}-2\,{{\rm e}^{{\it RootOf} \left ( -x{{\rm e}^{2\,{\it \_Z}}}+2\,x{{\rm e}^{{\it \_Z}}}+2\,{ {\rm e}^{{\it \_Z}}}+{\it \_C1}-2\,{\it \_Z}-x \right ) }} \right \} \]