ODE No. 800

\[ y'(x)=\frac {-b^3+6 b^2 x-12 b x^2-4 b y(x)^2+8 x^3+8 y(x)^3+8 x y(x)^2}{(2 x-b)^3} \] Mathematica : cpu = 0.422899 (sec), leaf count = 128

DSolve[Derivative[1][y][x] == (-b^3 + 6*b^2*x - 12*b*x^2 + 8*x^3 - 4*b*y[x]^2 + 8*x*y[x]^2 + 8*y[x]^3)/(-b + 2*x)^3,y[x],x]
 

\[\text {Solve}\left [-\frac {19}{3} \text {RootSum}\left [-19 \text {$\#$1}^3+6 \sqrt [3]{38} \text {$\#$1}-19\& ,\frac {\log \left (\frac {\frac {4}{(b-2 x)^2}-\frac {24 y(x)}{(b-2 x)^3}}{4 \sqrt [3]{38} \sqrt [3]{\frac {1}{(b-2 x)^6}}}-\text {$\#$1}\right )}{2 \sqrt [3]{38}-19 \text {$\#$1}^2}\& \right ]=\frac {1}{9} 38^{2/3} \left (\frac {1}{(b-2 x)^6}\right )^{2/3} (b-2 x)^4 \log (b-2 x)+c_1,y(x)\right ]\] Maple : cpu = 0.021 (sec), leaf count = 41

dsolve(diff(y(x),x) = (-b^3+6*b^2*x-12*b*x^2+8*x^3-4*b*y(x)^2+8*x*y(x)^2+8*y(x)^3)/(2*x-b)^3,y(x))
 

\[y \left (x \right ) = \frac {\RootOf \left (-\left (\int _{}^{\textit {\_Z}}\frac {1}{\textit {\_a}^{3}-\textit {\_a}^{2}-\textit {\_a} -1}d \textit {\_a} \right )+\ln \left (-2 x +b \right )+c_{1}\right ) \left (-2 x +b \right )}{2}\]