2.398 ODE No. 398
\[ y'(x)^2-3 x y(x)^{2/3} y'(x)+9 y(x)^{5/3}=0 \]
✓ Mathematica : cpu = 7.00597 (sec), leaf count = 413
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]
\[\left \{\text {Solve}\left [\frac {\sqrt {x^2-4 \sqrt [3]{y(x)}} \sqrt {x^2 y(x)^{4/3}-4 y(x)^{5/3}}}{8 y(x)-2 x^2 y(x)^{2/3}}+\frac {\sqrt {\left (x^2-4 \sqrt [3]{y(x)}\right ) y(x)^{4/3}} \log \left (\sqrt {x^2-4 \sqrt [3]{y(x)}}-x\right )}{\sqrt {x^2-4 \sqrt [3]{y(x)}} y(x)^{2/3}}+\log \left (4 y(x)^{4/3}-x^2 y(x)\right )-\log \left (x^2 \left (-y(x)^{2/3}\right )+\sqrt {x^2-4 \sqrt [3]{y(x)}} \sqrt {x^2 y(x)^{4/3}-4 y(x)^{5/3}}+4 y(x)\right )=c_1,y(x)\right ],\text {Solve}\left [\frac {1}{6} \left (\frac {3 \sqrt {x^2 y(x)^{4/3}-4 y(x)^{5/3}}}{\sqrt {x^2-4 \sqrt [3]{y(x)}} y(x)^{2/3}}+6 \log \left (4 y(x)^{4/3}-x^2 y(x)\right )-6 \log \left (x^2 y(x)^{2/3}+\sqrt {x^2-4 \sqrt [3]{y(x)}} \sqrt {x^2 y(x)^{4/3}-4 y(x)^{5/3}}-4 y(x)\right )\right )-\frac {\sqrt {\left (x^2-4 \sqrt [3]{y(x)}\right ) y(x)^{4/3}} \log \left (\sqrt {x^2-4 \sqrt [3]{y(x)}}-x\right )}{\sqrt {x^2-4 \sqrt [3]{y(x)}} y(x)^{2/3}}=c_1,y(x)\right ]\right \}\]
✓ Maple : cpu = 2.106 (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))
\[y \left (x \right ) = \frac {x^{6}}{64}\]