ODE No. 625

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

\[ y'(x)=\frac {1}{2} i x^2 \left (-2 \sqrt {6 y(x)-x^3}+i\right ) \] Mathematica : cpu = 0.287358 (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 = 0.232 (sec), leaf count = 53

\[ \left \{ \ln \left ( {x}^{3}-6\,y \left ( x \right ) -1 \right ) -2\,i\sqrt {-{x}^{3}+6\,y \left ( x \right ) }+2\,i\arctan \left ( \sqrt {-{x}^{3}+6\,y \left ( x \right ) } \right ) +2\,{x}^{3}-{\it \_C1}=0 \right \} \]