ODE No. 771

\[ y'(x)=\frac {-a^2 x^3-2 a b x^2-4 a x y(x)-4 a x+8}{2 a x^2+4 b x+8 y(x)+8} \] Mathematica : cpu = 0.046064 (sec), leaf count = 46

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

\[\left \{\left \{y(x)\to \frac {1}{4} \left (-a x^2-2 b x-4\right )-\frac {2 \left (1+W\left (-e^{-\frac {b^2 x}{4}-1+c_1}\right )\right )}{b}\right \}\right \}\] Maple : cpu = 0.294 (sec), leaf count = 84

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

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