\[ y'(x)^4-4 y(x) \left (x y'(x)-2 y(x)\right )^2=0 \] ✓ Mathematica : cpu = 3.17277 (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 = 0.254 (sec), leaf count = 118
\[\left \{\frac {\left (-x +\sqrt {x^{2}-4 \sqrt {y \left (x \right )}}\right )^{\frac {\sqrt {x^{2} y \left (x \right )-4 y \left (x \right )^{\frac {3}{2}}}}{\sqrt {x^{2}-4 \sqrt {y \left (x \right )}}\, \sqrt {y \left (x \right )}}} \left (x +\sqrt {x^{2}-4 \sqrt {y \left (x \right )}}\right )^{-\frac {\sqrt {x^{2} y \left (x \right )-4 y \left (x \right )^{\frac {3}{2}}}}{\sqrt {x^{2}-4 \sqrt {y \left (x \right )}}\, \sqrt {y \left (x \right )}}}}{\sqrt {y \left (x \right )}}-c_{1} = 0, y \left (x \right ) = \frac {x^{4}}{16}\right \}\]