\[ y'(x)=F\left (\frac {y(x)}{a+x}\right ) \] ✓ Mathematica : cpu = 15.4464 (sec), leaf count = 240
\[\text {Solve}\left [\int _1^{y(x)} \left (\frac {1}{-a F\left (\frac {K[2]}{a+x}\right )-x F\left (\frac {K[2]}{a+x}\right )+K[2]}-\int _1^x \left (\frac {F'\left (\frac {K[2]}{K[1]+a}\right )}{(K[1]+a) \left (a F\left (\frac {K[2]}{K[1]+a}\right )+K[1] F\left (\frac {K[2]}{K[1]+a}\right )-K[2]\right )}-\frac {F\left (\frac {K[2]}{K[1]+a}\right ) \left (\frac {a F'\left (\frac {K[2]}{K[1]+a}\right )}{K[1]+a}+\frac {K[1] F'\left (\frac {K[2]}{K[1]+a}\right )}{K[1]+a}-1\right )}{\left (a F\left (\frac {K[2]}{K[1]+a}\right )+K[1] F\left (\frac {K[2]}{K[1]+a}\right )-K[2]\right )^2}\right ) \, dK[1]\right ) \, dK[2]+\int _1^x \frac {F\left (\frac {y(x)}{K[1]+a}\right )}{a F\left (\frac {y(x)}{K[1]+a}\right )+K[1] F\left (\frac {y(x)}{K[1]+a}\right )-y(x)} \, dK[1]=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.036 (sec), leaf count = 28
\[ \left \{ y \left ( x \right ) =-{\it RootOf} \left ( \int ^{{\it \_Z}}\! \left ( F \left ( -{\it \_a} \right ) +{\it \_a} \right ) ^{-1}{d{\it \_a}}+\ln \left ( x+a \right ) +{\it \_C1} \right ) \left ( x+a \right ) \right \} \]