ODE No. 809

\[ y'(x)=\frac {64 x^3-240 x^2+64 x y(x)^2+64 y(x)^3-80 y(x)^2+300 x-125}{(4 x-5)^3} \] Mathematica : cpu = 0.340878 (sec), leaf count = 128

DSolve[Derivative[1][y][x] == (-125 + 300*x - 240*x^2 + 64*x^3 - 80*y[x]^2 + 64*x*y[x]^2 + 64*y[x]^3)/(-5 + 4*x)^3,y[x],x]
 

\[\text {Solve}\left [-\frac {19}{3} \text {RootSum}\left [-19 \text {$\#$1}^3+6 \sqrt [3]{38} \text {$\#$1}-19\& ,\frac {\log \left (\frac {\frac {192 y(x)}{(4 x-5)^3}+\frac {16}{(4 x-5)^2}}{16 \sqrt [3]{38} \sqrt [3]{\frac {1}{(4 x-5)^6}}}-\text {$\#$1}\right )}{2 \sqrt [3]{38}-19 \text {$\#$1}^2}\& \right ]=\frac {1}{9} 38^{2/3} \left (\frac {1}{(5-4 x)^6}\right )^{2/3} (5-4 x)^4 \log (5-4 x)+c_1,y(x)\right ]\] Maple : cpu = 0.019 (sec), leaf count = 41

dsolve(diff(y(x),x) = (-125+300*x-240*x^2+64*x^3-80*y(x)^2+64*x*y(x)^2+64*y(x)^3)/(4*x-5)^3,y(x))
 

\[y \left (x \right ) = -\frac {\RootOf \left (-\left (\int _{}^{\textit {\_Z}}\frac {1}{\textit {\_a}^{3}-\textit {\_a}^{2}-\textit {\_a} -1}d \textit {\_a} \right )+\ln \left (4 x -5\right )+c_{1}\right ) \left (4 x -5\right )}{4}\]