2.547 ODE No. 547
\[ y'(x)^4-4 y(x) \left (x y'(x)-2 y(x)\right )^2=0 \]
✓ Mathematica : cpu = 5.18094 (sec), leaf count = 763
DSolve[Derivative[1][y][x]^4 - 4*y[x]*(-2*y[x] + x*Derivative[1][y][x])^2 == 0,y[x],x]
\[\left \{\text {Solve}\left [\frac {\sqrt {x^2-4 \sqrt {y(x)}} \sqrt {x^2 y(x)-4 y(x)^{3/2}}}{8 y(x)-2 x^2 \sqrt {y(x)}}+\frac {\sqrt {\left (x^2-4 \sqrt {y(x)}\right ) y(x)} \log \left (\sqrt {x^2-4 \sqrt {y(x)}}-x\right )}{\sqrt {x^2-4 \sqrt {y(x)}} \sqrt {y(x)}}+\log \left (4 y(x)^{3/2}-x^2 y(x)\right )-\log \left (x^2 \left (-\sqrt {y(x)}\right )+\sqrt {x^2-4 \sqrt {y(x)}} \sqrt {x^2 y(x)-4 y(x)^{3/2}}+4 y(x)\right )=c_1,y(x)\right ],\text {Solve}\left [\frac {\sqrt {\left (x^2+4 \sqrt {y(x)}\right ) y(x)} \log \left (\sqrt {x^2+4 \sqrt {y(x)}}-x\right )}{\sqrt {x^2+4 \sqrt {y(x)}} \sqrt {y(x)}}+\frac {1}{4} \left (-\frac {2 \sqrt {x^2+4 \sqrt {y(x)}} \sqrt {y(x)}}{\sqrt {\left (x^2+4 \sqrt {y(x)}\right ) y(x)}}+4 \log \left (\sqrt {x^2+4 \sqrt {y(x)}} y(x)\right )-4 \log \left (\sqrt {\left (x^2+4 \sqrt {y(x)}\right ) y(x)}-\sqrt {x^2+4 \sqrt {y(x)}} \sqrt {y(x)}\right )\right )=c_1,y(x)\right ],\text {Solve}\left [\frac {1}{4} \left (\frac {2 \sqrt {x^2+4 \sqrt {y(x)}} \sqrt {y(x)}}{\sqrt {\left (x^2+4 \sqrt {y(x)}\right ) y(x)}}+4 \log \left (\sqrt {x^2+4 \sqrt {y(x)}} y(x)\right )-4 \log \left (\sqrt {x^2+4 \sqrt {y(x)}} \sqrt {y(x)}+\sqrt {\left (x^2+4 \sqrt {y(x)}\right ) y(x)}\right )\right )-\frac {\sqrt {\left (x^2+4 \sqrt {y(x)}\right ) y(x)} \log \left (\sqrt {x^2+4 \sqrt {y(x)}}-x\right )}{\sqrt {x^2+4 \sqrt {y(x)}} \sqrt {y(x)}}=c_1,y(x)\right ],\text {Solve}\left [\frac {1}{4} \left (\frac {2 \sqrt {x^2 y(x)-4 y(x)^{3/2}}}{\sqrt {x^2-4 \sqrt {y(x)}} \sqrt {y(x)}}+4 \log \left (4 y(x)^{3/2}-x^2 y(x)\right )-4 \log \left (x^2 \sqrt {y(x)}+\sqrt {x^2-4 \sqrt {y(x)}} \sqrt {x^2 y(x)-4 y(x)^{3/2}}-4 y(x)\right )\right )-\frac {\sqrt {\left (x^2-4 \sqrt {y(x)}\right ) y(x)} \log \left (\sqrt {x^2-4 \sqrt {y(x)}}-x\right )}{\sqrt {x^2-4 \sqrt {y(x)}} \sqrt {y(x)}}=c_1,y(x)\right ]\right \}\]
✓ Maple : cpu = 0.245 (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))
\[y \left (x \right ) = \frac {x^{4}}{16}\]