2.625   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 = 0.375532 (sec), leaf count = 67

\[\text {Solve}\left [12 i c_1+2 \sqrt {6 y(x)-x^3}+i \log \left (-x^3+6 y(x)+1\right )+2 i x^3=2 \tan ^{-1}\left (\sqrt {6 y(x)-x^3}\right ),y(x)\right ]\]

Maple : cpu = 4.48 (sec), leaf count = 55

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