2.333   ODE No. 333

\[ -x^{3/2} y(x)^{5/2}+\left (2 x^{5/2} y(x)^{3/2}+x^2 y(x)-x\right ) y'(x)+x y(x)^2-y(x)=0 \] Mathematica : cpu = 0.4241 (sec), leaf count = 72


\[\text {Solve}\left [\frac {2 \sqrt {x y(x)} \log (y(x))}{\sqrt {x} \sqrt {y(x)}}-\frac {\sqrt {x y(x)} \left (3 x^{3/2} y(x)^{3/2} \log (x)+6 x y(x)-2\right )}{3 x^2 y(x)^2}=c_1,y(x)\right ]\] Maple : cpu = 0.097 (sec), leaf count = 32


\[\ln \left (y \relax (x )\right )+\frac {1}{3 x^{\frac {3}{2}} y \relax (x )^{\frac {3}{2}}}-\frac {1}{\sqrt {x}\, \sqrt {y \relax (x )}}-\frac {\ln \relax (x )}{2}-c_{1} = 0\]