2.333   ODE No. 333

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

\[ \left (2 x^{5/2} y(x)^{3/2}+x^2 y(x)-x\right ) y'(x)-x^{3/2} y(x)^{5/2}+x y(x)^2-y(x)=0 \] Mathematica : cpu = 0.307226 (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 = 0.076 (sec), leaf count = 32

\[ \left \{ \ln \left ( y \left ( x \right ) \right ) +{\frac {1}{3} \left ( y \left ( x \right ) \right ) ^{-{\frac {3}{2}}}{x}^{-{\frac {3}{2}}}}-{{\frac {1}{\sqrt {x}}}{\frac {1}{\sqrt {y \left ( x \right ) }}}}-{\frac {\ln \left ( x \right ) }{2}}-{\it \_C1}=0 \right \} \]