2.333   ODE No. 333

  1. Problem in Latex
  2. Mathematica input
  3. Maple input

\[ -x^{3/2} y(x)^{5/2}+\left (2 x^{5/2} y(x)^{3/2}+x^2 y(x)-x\right ) y'(x)+x y(x)^2-y(x)=0 \] Mathematica : cpu = 0.492765 (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 = 0.104 (sec), leaf count = 32

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