ODE No. 398

$$y^{\prime }(x{)}^2-3xy(x{)}^{2/3}{y}^{\prime }(x)+9y(x{)}^{5/3}=0$$ ✓ 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]
 

$$\{\text{Solve}[-\frac{{(x^2-4\sqrt[3]{y(x)})}^{3/2}y(x{)}^2\log (y(x))}{6{((x^2-4\sqrt[3]{y(x)})y(x{)}^{4/3})}^{3/2}}+\frac{\sqrt{(x^2-4\sqrt[3]{y(x)})y(x{)}^{4/3}}\log (\sqrt{x^2-4\sqrt[3]{y(x)}}+x)}{\sqrt{x^2-4\sqrt[3]{y(x)}}y(x{)}^{2/3}}+\frac{1}{6}\log (y(x))=c_1,y(x)],\text{Solve}[\frac{1}{6}(\frac{{(x^2-4\sqrt[3]{y(x)})}^{3/2}y(x{)}^2\log (y(x))}{{((x^2-4\sqrt[3]{y(x)})y(x{)}^{4/3})}^{3/2}}+\log (y(x)))-\frac{\sqrt{(x^2-4\sqrt[3]{y(x)})y(x{)}^{4/3}}\log (\sqrt{x^2-4\sqrt[3]{y(x)}}+x)}{\sqrt{x^2-4\sqrt[3]{y(x)}}y(x{)}^{2/3}}=c_1,y(x)]\}$$ ✓ 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))
 

$$y\left(x\right)=\frac{x^6}{64}$$