ODE No. 757

\[ y'(x)=\frac {x^3+2 x^2-4 x y(x)-4 x-8}{2 x^2-8 y(x)+4 x-8} \] Mathematica : cpu = 0.0365716 (sec), leaf count = 36

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

\[\left \{\left \{y(x)\to \frac {1}{4} \left (x^2+2 x-4\right )+2 \left (1+W\left (-e^{-\frac {x}{4}-1+c_1}\right )\right )\right \}\right \}\] Maple : cpu = 0.121 (sec), leaf count = 26

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

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