\[ y'(x)=F\left (\frac {y(x)}{a+x}\right ) \] ✓ Mathematica : cpu = 15.2591 (sec), leaf count = 141
\[\text {Solve}\left [c_1=\int _1^{y(x)} \left (\frac {1}{K[2]-(a+x) F\left (\frac {K[2]}{a+x}\right )}-\int _1^x \frac {(K[1]+a) F\left (\frac {K[2]}{K[1]+a}\right )-K[2] F'\left (\frac {K[2]}{K[1]+a}\right )}{(K[1]+a) \left (K[2]-(K[1]+a) F\left (\frac {K[2]}{K[1]+a}\right )\right )^2} \, dK[1]\right ) \, dK[2]+\int _1^x \frac {F\left (\frac {y(x)}{K[1]+a}\right )}{(K[1]+a) F\left (\frac {y(x)}{K[1]+a}\right )-y(x)} \, dK[1],y(x)\right ]\]
✓ Maple : cpu = 1.804 (sec), leaf count = 28
\[ \left \{ y \left ( x \right ) =-{\it RootOf} \left ( \int ^{{\it \_Z}}\! \left ( F \left ( -{\it \_a} \right ) +{\it \_a} \right ) ^{-1}{d{\it \_a}}+\ln \left ( x+a \right ) +{\it \_C1} \right ) \left ( x+a \right ) \right \} \]