\[ y'(x)^4-4 y(x) \left (x y'(x)-2 y(x)\right )^2=0 \] ✓ Mathematica : cpu = 19.4573 (sec), leaf count = 503
DSolve[Derivative[1][y][x]^4 - 4*y[x]*(-2*y[x] + x*Derivative[1][y][x])^2 == 0,y[x],x]
\[\left \{\text {Solve}\left [\frac {\sqrt {\left (x^2+4 \sqrt {y(x)}\right ) y(x)} \log \left (\sqrt {x^2+4 \sqrt {y(x)}}-x\right )}{\sqrt {x^2+4 \sqrt {y(x)}} \sqrt {y(x)}}+\frac {1}{4} \left (\log (y(x))-\frac {\sqrt {x^2+4 \sqrt {y(x)}} \sqrt {y(x)} \log (y(x))}{\sqrt {\left (x^2+4 \sqrt {y(x)}\right ) y(x)}}\right )=c_1,y(x)\right ],\text {Solve}\left [\frac {1}{4} \left (\frac {\sqrt {x^2+4 \sqrt {y(x)}} \sqrt {y(x)} \log (y(x))}{\sqrt {\left (x^2+4 \sqrt {y(x)}\right ) y(x)}}+\log (y(x))\right )-\frac {\sqrt {\left (x^2+4 \sqrt {y(x)}\right ) y(x)} \log \left (\sqrt {x^2+4 \sqrt {y(x)}}-x\right )}{\sqrt {x^2+4 \sqrt {y(x)}} \sqrt {y(x)}}=c_1,y(x)\right ],\text {Solve}\left [\frac {1}{2} \left (\frac {\sqrt {x^2-4 \sqrt {y(x)}} \sqrt {y(x)} \log (y(x))}{2 \sqrt {x^2 y(x)-4 y(x)^{3/2}}}+\frac {1}{2} \log (y(x))\right )-\frac {\sqrt {\left (x^2-4 \sqrt {y(x)}\right ) y(x)} \log \left (\sqrt {x^2-4 \sqrt {y(x)}}-x\right )}{\sqrt {x^2-4 \sqrt {y(x)}} \sqrt {y(x)}}=c_1,y(x)\right ],\text {Solve}\left [\frac {\sqrt {\left (x^2-4 \sqrt {y(x)}\right ) y(x)} \log \left (\sqrt {x^2-4 \sqrt {y(x)}}-x\right )}{\sqrt {x^2-4 \sqrt {y(x)}} \sqrt {y(x)}}+\left (\frac {1}{4}-\frac {\sqrt {x^2 y(x)-4 y(x)^{3/2}}}{4 \sqrt {x^2-4 \sqrt {y(x)}} \sqrt {y(x)}}\right ) \log (y(x))=c_1,y(x)\right ]\right \}\] ✓ Maple : cpu = 0.214 (sec), leaf count = 118
dsolve(diff(y(x),x)^4-4*y(x)*(x*diff(y(x),x)-2*y(x))^2=0,y(x))
\[y \left (x \right ) = \frac {x^{4}}{16}\]