3.800   ODE No. 800

\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {-{b}^{3}+6\,{b}^{2}x-12\,b{x}^{2}+8\,{x}^{3}-4\,b \left ( y \left ( x \right ) \right ) ^{2}+8\,x \left ( y \left ( x \right ) \right ) ^{2}+8\, \left ( y \left ( x \right ) \right ) ^{3}}{ \left ( 2\,x-b \right ) ^{3}}}=0} \]

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

Mathematica: cpu = 0.176022 (sec), leaf count = 128 \[ \text {Solve}\left [-\frac {19}{3} \text {RootSum}\left [-19 \text {$\#$1}^3+6 \sqrt [3]{38} \text {$\#$1}-19\& ,\frac {\log \left (\frac {\frac {4}{(b-2 x)^2}-\frac {24 y(x)}{(b-2 x)^3}}{4 \sqrt [3]{38} \sqrt [3]{\frac {1}{(b-2 x)^6}}}-\text {$\#$1}\right )}{2 \sqrt [3]{38}-19 \text {$\#$1}^2}\& \right ]=\frac {1}{9} 38^{2/3} \left (\frac {1}{(b-2 x)^6}\right )^{2/3} (b-2 x)^4 \log (b-2 x)+c_1,y(x)\right ] \]

Maple: cpu = 0.015 (sec), leaf count = 41 \[ \left \{ y \left ( x \right ) ={\frac {{\it RootOf} \left ( -\int ^{{\it \_Z}}\! \left ( {{\it \_a}}^{3}-{{\it \_a}}^{2}-{\it \_a}-1 \right ) ^{- 1}{d{\it \_a}}+\ln \left ( -2\,x+b \right ) +{\it \_C1} \right ) \left ( -2\,x+b \right ) }{2}} \right \} \]