#### 2.577   ODE No. 577

$y'(x)=F\left (\frac {y(x)}{a+x}\right )$ Mathematica : cpu = 0.242657 (sec), leaf count = 243

$\text {Solve}\left [\int _1^{y(x)}\left (\frac {1}{-a F\left (\frac {K[2]}{a+x}\right )-x F\left (\frac {K[2]}{a+x}\right )+K[2]}-\int _1^x\left (\frac {F'\left (\frac {K[2]}{a+K[1]}\right )}{(a+K[1]) \left (a F\left (\frac {K[2]}{a+K[1]}\right )+K[1] F\left (\frac {K[2]}{a+K[1]}\right )-K[2]\right )}-\frac {F\left (\frac {K[2]}{a+K[1]}\right ) \left (\frac {a F'\left (\frac {K[2]}{a+K[1]}\right )}{a+K[1]}+\frac {K[1] F'\left (\frac {K[2]}{a+K[1]}\right )}{a+K[1]}-1\right )}{\left (a F\left (\frac {K[2]}{a+K[1]}\right )+K[1] F\left (\frac {K[2]}{a+K[1]}\right )-K[2]\right )^2}\right )dK[1]\right )dK[2]+\int _1^x\frac {F\left (\frac {y(x)}{a+K[1]}\right )}{a F\left (\frac {y(x)}{a+K[1]}\right )+K[1] F\left (\frac {y(x)}{a+K[1]}\right )-y(x)}dK[1]=c_1,y(x)\right ]$ Maple : cpu = 0.025 (sec), leaf count = 28

$\left \{ y \left ( x \right ) =-{\it RootOf} \left ( \int ^{{\it \_Z}}\! \left ( F \left ( -{\it \_a} \right ) +{\it \_a} \right ) ^{-1}{d{\it \_a}}+\ln \left ( x+a \right ) +{\it \_C1} \right ) \left ( x+a \right ) \right \}$