\[ \boxed { \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{4}-4\,y \left ( x \right ) \left ( x{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -2\,y \left ( x \right ) \right ) ^{2}=0} \]
Mathematica: cpu = 1.233157 (sec), leaf count = 490 \[ \left \{\text {Solve}\left [\frac {\sqrt {\left (x^2-4 \sqrt {y(x)}\right ) y(x)} \log \left (\sqrt {x^2-4 \sqrt {y(x)}}+x\right )}{\sqrt {x^2-4 \sqrt {y(x)}} \sqrt {y(x)}}-\frac {\sqrt {x^2-4 \sqrt {y(x)}} \sqrt {y(x)} \log (y(x))}{4 \sqrt {\left (x^2-4 \sqrt {y(x)}\right ) y(x)}}+\frac {1}{4} \log (y(x))=c_1,y(x)\right ],\text {Solve}\left [\frac {1}{4} \left (\frac {\sqrt {x^2-4 \sqrt {y(x)}} \sqrt {y(x)} \log (y(x))}{\sqrt {\left (x^2-4 \sqrt {y(x)}\right ) y(x)}}+\log (y(x))\right )-\frac {\sqrt {\left (x^2-4 \sqrt {y(x)}\right ) y(x)} \log \left (\sqrt {x^2-4 \sqrt {y(x)}}+x\right )}{\sqrt {x^2-4 \sqrt {y(x)}} \sqrt {y(x)}}=c_1,y(x)\right ],\text {Solve}\left [\frac {\sqrt {\left (x^2+4 \sqrt {y(x)}\right ) y(x)} \log \left (\sqrt {x^2+4 \sqrt {y(x)}}+x\right )}{\sqrt {x^2+4 \sqrt {y(x)}} \sqrt {y(x)}}+\frac {1}{4} \left (\log (y(x))-\frac {\sqrt {x^2+4 \sqrt {y(x)}} \sqrt {y(x)} \log (y(x))}{\sqrt {\left (x^2+4 \sqrt {y(x)}\right ) y(x)}}\right )=c_1,y(x)\right ],\text {Solve}\left [\frac {1}{4} \left (\frac {\sqrt {x^2+4 \sqrt {y(x)}} \sqrt {y(x)} \log (y(x))}{\sqrt {\left (x^2+4 \sqrt {y(x)}\right ) y(x)}}+\log (y(x))\right )-\frac {\sqrt {\left (x^2+4 \sqrt {y(x)}\right ) y(x)} \log \left (\sqrt {x^2+4 \sqrt {y(x)}}+x\right )}{\sqrt {x^2+4 \sqrt {y(x)}} \sqrt {y(x)}}=c_1,y(x)\right ]\right \} \]
Maple: cpu = 0.171 (sec), leaf count = 118 \[ \left \{ {1\sqrt {y \left ( x \right ) } \left ( \sqrt {{x}^{2}-4\,\sqrt {y \left ( x \right ) }}+x \right ) ^{{1\sqrt {{x}^{2}y \left ( x \right ) -4\, \left ( y \left ( x \right ) \right ) ^{3/2}}{\frac {1}{\sqrt {{x}^{ 2}-4\,\sqrt {y \left ( x \right ) }}}}{\frac {1}{\sqrt {y \left ( x \right ) }}}}} \left ( \left ( \sqrt {{x}^{2}-4\,\sqrt {y \left ( x \right ) }}-x \right ) ^{{1\sqrt {{x}^{2}y \left ( x \right ) -4\, \left ( y \left ( x \right ) \right ) ^{3/2}}{\frac {1}{\sqrt {{x}^{2}-4 \,\sqrt {y \left ( x \right ) }}}}{\frac {1}{\sqrt {y \left ( x \right ) } }}}} \right ) ^{-1}}-{\it \_C1}=0,y \left ( x \right ) ={\frac {{x}^{4}}{ 16}} \right \} \]