2.664   ODE No. 664

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

\[ y'(x)=x^2 \sqrt {x^2+4 y(x)-4 x}-\frac {x}{2}+1 \] Mathematica : cpu = 0.543652 (sec), leaf count = 94

\[\text {Solve}\left [-\frac {1}{2} \sqrt {x^2+4 y(x)-4 x}+\log \left (-\sqrt {x^2+4 y(x)-4 x}-x+2\right )-\tanh ^{-1}\left (\frac {2 x-4}{2 \sqrt {x^2+4 y(x)-4 x}}\right )+\frac {x^3}{3}-\frac {1}{2} \log (2-2 y(x))=c_1,y(x)\right ]\] Maple : cpu = 0.393 (sec), leaf count = 25

\[ \left \{ {\it \_C1}+{\frac {2\,{x}^{3}}{3}}-\sqrt {{x}^{2}-4\,x+4\,y \left ( x \right ) }=0 \right \} \]