\[ y'(x)^2-3 x y(x)^{2/3} y'(x)+9 y(x)^{5/3}=0 \] ✓ Mathematica : cpu = 11.4215 (sec), leaf count = 696
DSolve[9*y[x]^(5/3) - 3*x*y[x]^(2/3)*Derivative[1][y][x] + Derivative[1][y][x]^2 == 0,y[x],x]
\[\left \{\text {Solve}\left [\frac {8 x^2 \log (y(x))-6 \sqrt {x^4} \log \left (x^2 \sqrt {x^2-4 \sqrt [3]{y(x)}}\right )-3 \sqrt {x^4} \log \left (4 \sqrt [3]{y(x)}-x^2\right )+6 \left (\sqrt {x^4}-x^2\right ) \log \left (16 x^2 \sqrt {x^2 y(x)^{4/3}-4 y(x)^{5/3}}+x^6 \left (-\sqrt {x^2-4 \sqrt [3]{y(x)}}\right )-\sqrt {x^4} \sqrt {x^2-4 \sqrt [3]{y(x)}} \left (x^4-16 y(x)^{2/3}\right )\right )+6 \left (\sqrt {x^4}+x^2\right ) \log \left (16 x^2 \sqrt {x^2 y(x)^{4/3}-4 y(x)^{5/3}}+x^6 \sqrt {x^2-4 \sqrt [3]{y(x)}}-\sqrt {x^4} \sqrt {x^2-4 \sqrt [3]{y(x)}} \left (x^4-16 y(x)^{2/3}\right )\right )}{48 x^2}-\frac {\sqrt {\left (x^2-4 \sqrt [3]{y(x)}\right ) y(x)^{4/3}} \log \left (\sqrt {x^2-4 \sqrt [3]{y(x)}}-x\right )}{\sqrt {x^2-4 \sqrt [3]{y(x)}} y(x)^{2/3}}=c_1,y(x)\right ],\text {Solve}\left [\frac {\sqrt {\left (x^2-4 \sqrt [3]{y(x)}\right ) y(x)^{4/3}} \log \left (\sqrt {x^2-4 \sqrt [3]{y(x)}}-x\right )}{\sqrt {x^2-4 \sqrt [3]{y(x)}} y(x)^{2/3}}+\frac {8 x^2 \log (y(x))+6 \sqrt {x^4} \log \left (x^2 \sqrt {x^2-4 \sqrt [3]{y(x)}}\right )+3 \sqrt {x^4} \log \left (4 \sqrt [3]{y(x)}-x^2\right )+6 \left (x^2-\sqrt {x^4}\right ) \log \left (16 x^2 \sqrt {x^2 y(x)^{4/3}-4 y(x)^{5/3}}+x^6 \left (-\sqrt {x^2-4 \sqrt [3]{y(x)}}\right )-\sqrt {x^4} \sqrt {x^2-4 \sqrt [3]{y(x)}} \left (x^4-16 y(x)^{2/3}\right )\right )-6 \left (\sqrt {x^4}+x^2\right ) \log \left (16 x^2 \sqrt {x^2 y(x)^{4/3}-4 y(x)^{5/3}}+x^6 \sqrt {x^2-4 \sqrt [3]{y(x)}}-\sqrt {x^4} \sqrt {x^2-4 \sqrt [3]{y(x)}} \left (x^4-16 y(x)^{2/3}\right )\right )}{48 x^2}=c_1,y(x)\right ]\right \}\] ✓ Maple : cpu = 1.979 (sec), leaf count = 138
dsolve(diff(y(x),x)^2-3*x*y(x)^(2/3)*diff(y(x),x)+9*y(x)^(5/3) = 0,y(x))
\[y \left (x \right ) = \frac {x^{6}}{64}\]