\[ y'(x)^2-3 x y(x)^{2/3} y'(x)+9 y(x)^{5/3}=0 \] ✓ Mathematica : cpu = 1.52946 (sec), leaf count = 258
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]
\[\left \{\text {Solve}\left [-\frac {\left (x^2-4 \sqrt [3]{y(x)}\right )^{3/2} y(x)^2 \log (y(x))}{6 \left (\left (x^2-4 \sqrt [3]{y(x)}\right ) y(x)^{4/3}\right )^{3/2}}+\frac {\sqrt {\left (x^2-4 \sqrt [3]{y(x)}\right ) y(x)^{4/3}} \log \left (\sqrt {x^2-4 \sqrt [3]{y(x)}}+x\right )}{\sqrt {x^2-4 \sqrt [3]{y(x)}} y(x)^{2/3}}+\frac {1}{6} \log (y(x))=c_1,y(x)\right ],\text {Solve}\left [\frac {1}{6} \left (\frac {\left (x^2-4 \sqrt [3]{y(x)}\right )^{3/2} y(x)^2 \log (y(x))}{\left (\left (x^2-4 \sqrt [3]{y(x)}\right ) y(x)^{4/3}\right )^{3/2}}+\log (y(x))\right )-\frac {\sqrt {\left (x^2-4 \sqrt [3]{y(x)}\right ) y(x)^{4/3}} \log \left (\sqrt {x^2-4 \sqrt [3]{y(x)}}+x\right )}{\sqrt {x^2-4 \sqrt [3]{y(x)}} y(x)^{2/3}}=c_1,y(x)\right ]\right \}\] ✓ Maple : cpu = 2.128 (sec), leaf count = 137
dsolve(diff(y(x),x)^2-3*x*y(x)^(2/3)*diff(y(x),x)+9*y(x)^(5/3) = 0,y(x))
\[y \left (x \right ) = \frac {x^{6}}{64}\]