3.625   ODE No. 625

\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =i/2{x}^{2} \left ( i-2\,\sqrt {-{x}^{3}+6\,y \left ( x \right ) } \right ) =0} \]

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

Mathematica: cpu = 0.209527 (sec), leaf count = 76 \[ \text {Solve}\left [-y(x)+\frac {1}{12} \left (2 i \sqrt {6 y(x)-x^3}-\log \left (-x^3+6 y(x)+1\right )-2 i \tan ^{-1}\left (\sqrt {6 y(x)-x^3}\right )-2 x^3+12 y(x)\right )=c_1,y(x)\right ] \]

Maple: cpu = 0.156 (sec), leaf count = 53 \[ \left \{ -2\,i\sqrt {-{x}^{3}+6\,y \left ( x \right ) }+2\,i\arctan \left ( \sqrt {-{x}^{3}+6\,y \left ( x \right ) } \right ) +\ln \left ( { x}^{3}-6\,y \left ( x \right ) -1 \right ) +2\,{x}^{3}-{\it \_C1}=0 \right \} \]