2.577   ODE No. 577

1. Problem in Latex
2. Mathematica input
3. Maple input

$$y^{\prime }(x)=F\left(\frac{y(x)}{a+x}\right)$$ ✓ Mathematica : cpu = 0.27311 (sec), leaf count = 243

$$\text{Solve}[{\int }_1^{y(x)}(\frac{1}{-aF\left(\frac{K[2]}{a+x}\right)-xF\left(\frac{K[2]}{a+x}\right)+K[2]}-{\int }_1^x(\frac{F^{\prime }\left(\frac{K[2]}{a+K[1]}\right)}{(a+K[1])(aF\left(\frac{K[2]}{a+K[1]}\right)+K[1]F\left(\frac{K[2]}{a+K[1]}\right)-K[2])}-\frac{F\left(\frac{K[2]}{a+K[1]}\right)(\frac{a{F}^{\prime }\left(\frac{K[2]}{a+K[1]}\right)}{a+K[1]}+\frac{K[1]F^{\prime }\left(\frac{K[2]}{a+K[1]}\right)}{a+K[1]}-1)}{{(aF\left(\frac{K[2]}{a+K[1]}\right)+K[1]F\left(\frac{K[2]}{a+K[1]}\right)-K[2])}^2})dK[1])dK[2]+{\int }_1^x\frac{F\left(\frac{y(x)}{a+K[1]}\right)}{aF\left(\frac{y(x)}{a+K[1]}\right)+K[1]F\left(\frac{y(x)}{a+K[1]}\right)-y(x)}dK[1]=c_1,y(x)]$$ ✓ Maple : cpu = 0.102 (sec), leaf count = 28

$$\{y\left(x\right)=-\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}({\int }^{\mathit{\_}\mathit{Z}}{(F(-\mathit{\_}\mathit{a})+\mathit{\_}\mathit{a})}^{-1}d\mathit{\_}\mathit{a}+\ln (x+a)+\mathit{\_}\mathit{C}\mathit{1})(x+a)\}$$