\[ y'(x)=F\left (\frac {a x^2}{4}+\frac {b x}{2}+y(x)\right )-\frac {a x}{2} \] ✓ Mathematica : cpu = 17.8942 (sec), leaf count = 162
\[\text {Solve}\left [c_1=\int _1^{y(x)} \left (-\int _1^x \frac {2 (a K[1]+b) F'\left (\frac {1}{4} a K[1]^2+\frac {1}{2} b K[1]+K[2]\right )}{\left (2 F\left (\frac {1}{4} a K[1]^2+\frac {1}{2} b K[1]+K[2]\right )+b\right )^2} \, dK[1]-\frac {2}{2 F\left (K[2]+\frac {a x^2}{4}+\frac {b x}{2}\right )+b}\right ) \, dK[2]+\int _1^x \frac {2 F\left (\frac {1}{4} K[1] (a K[1]+2 b)+y(x)\right )-a K[1]}{2 F\left (\frac {1}{4} K[1] (a K[1]+2 b)+y(x)\right )+b} \, dK[1],y(x)\right ]\]
✓ Maple : cpu = 0.135 (sec), leaf count = 35
\[ \left \{ y \left ( x \right ) =-{\frac {a{x}^{2}}{4}}-{\frac {bx}{2}}+{\it RootOf} \left ( -x+2\,\int ^{{\it \_Z}}\! \left ( 2\,F \left ( {\it \_a} \right ) +b \right ) ^{-1}{d{\it \_a}}+{\it \_C1} \right ) \right \} \]