2.546   ODE No. 546

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

\[ y'(x)^4+3 (x-1) y'(x)^2-3 (2 y(x)-1) y'(x)+3 x=0 \] Mathematica : cpu = 3601.4 (sec), leaf count = 0 , timed out

$Aborted

Maple : cpu = 0.141 (sec), leaf count = 245

\[ \left \{ y \left ( x \right ) =-x+{\frac {5}{6}},y \left ( x \right ) =x+{\frac {1}{6}},y \left ( x \right ) ={\frac {x}{6} \left ( 3\, \left ( -{\it \_C1}/2-1/2\,\sqrt {{{\it \_C1}}^{2}+4\,x} \right ) ^{2}+3 \right ) \left ( -{\frac {{\it \_C1}}{2}}-{\frac {1}{2}\sqrt {{{\it \_C1}}^{2}+4\,x}} \right ) ^{-1}}+{\frac {1}{6} \left ( \left ( -{\frac {{\it \_C1}}{2}}-{\frac {1}{2}\sqrt {{{\it \_C1}}^{2}+4\,x}} \right ) ^{4}-3\, \left ( -{\it \_C1}/2-1/2\,\sqrt {{{\it \_C1}}^{2}+4\,x} \right ) ^{2}-{\frac {3\,{\it \_C1}}{2}}-{\frac {3}{2}\sqrt {{{\it \_C1}}^{2}+4\,x}} \right ) \left ( -{\frac {{\it \_C1}}{2}}-{\frac {1}{2}\sqrt {{{\it \_C1}}^{2}+4\,x}} \right ) ^{-1}},y \left ( x \right ) ={\frac {x}{6} \left ( 3\, \left ( -{\it \_C1}/2+1/2\,\sqrt {{{\it \_C1}}^{2}+4\,x} \right ) ^{2}+3 \right ) \left ( -{\frac {{\it \_C1}}{2}}+{\frac {1}{2}\sqrt {{{\it \_C1}}^{2}+4\,x}} \right ) ^{-1}}+{\frac {1}{6} \left ( \left ( -{\frac {{\it \_C1}}{2}}+{\frac {1}{2}\sqrt {{{\it \_C1}}^{2}+4\,x}} \right ) ^{4}-3\, \left ( -{\it \_C1}/2+1/2\,\sqrt {{{\it \_C1}}^{2}+4\,x} \right ) ^{2}-{\frac {3\,{\it \_C1}}{2}}+{\frac {3}{2}\sqrt {{{\it \_C1}}^{2}+4\,x}} \right ) \left ( -{\frac {{\it \_C1}}{2}}+{\frac {1}{2}\sqrt {{{\it \_C1}}^{2}+4\,x}} \right ) ^{-1}} \right \} \]