ODE No. 767

\[ y'(x)=\frac {-x^3+2 x^2-8 x y(x)-8 x+32}{4 x^2+32 y(x)-8 x+32} \] Mathematica : cpu = 0.036282 (sec), leaf count = 38

DSolve[Derivative[1][y][x] == (32 - 8*x + 2*x^2 - x^3 - 8*x*y[x])/(32 - 8*x + 4*x^2 + 32*y[x]),y[x],x]
 

\[\left \{\left \{y(x)\to \frac {1}{8} \left (-x^2+2 x-8\right )+4 \left (1+W\left (-e^{-\frac {x}{16}-1+c_1}\right )\right )\right \}\right \}\] Maple : cpu = 0.117 (sec), leaf count = 26

dsolve(diff(y(x),x) = (-8*x*y(x)-x^3+2*x^2-8*x+32)/(32*y(x)+4*x^2-8*x+32),y(x))
 

\[y \left (x \right ) = -\frac {x^{2}}{8}+4 \LambertW \left (\frac {c_{1} {\mathrm e}^{-\frac {x}{16}} {\mathrm e}^{-\frac {3}{4}}}{4}\right )+\frac {x}{4}+3\]