3.577   ODE No. 577

$$\boxed{{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)=F\left(\frac{y\left(x\right)}{x+a}\right)=0}}$$

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

Mathematica: cpu = 12.111538 (sec), leaf count = 240 $$\text{Solve}[{\int }_1^{y(x)}(\frac{1}{-aF\left(\frac{K[2]}{a+x}\right)-xF\left(\frac{K[2]}{a+x}\right)+K[2]}-{\int }_1^x(\frac{F^{\prime }\left(\frac{K[2]}{K[1]+a}\right)}{(K[1]+a)(aF\left(\frac{K[2]}{K[1]+a}\right)+K[1]F\left(\frac{K[2]}{K[1]+a}\right)-K[2])}-\frac{F\left(\frac{K[2]}{K[1]+a}\right)(\frac{a{F}^{\prime }\left(\frac{K[2]}{K[1]+a}\right)}{K[1]+a}+\frac{K[1]F^{\prime }\left(\frac{K[2]}{K[1]+a}\right)}{K[1]+a}-1)}{{(aF\left(\frac{K[2]}{K[1]+a}\right)+K[1]F\left(\frac{K[2]}{K[1]+a}\right)-K[2])}^2})dK[1])dK[2]+{\int }_1^x\frac{F\left(\frac{y(x)}{K[1]+a}\right)}{aF\left(\frac{y(x)}{K[1]+a}\right)+K[1]F\left(\frac{y(x)}{K[1]+a}\right)-y(x)}dK[1]=c_1,y(x)]$$

Maple: cpu = 0.031 (sec), leaf count = 28 $$\{y\left(x\right)=-\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}({\int }^{\mathit{\_}\mathit{Z}}{(F(-\mathit{\_}\mathit{a})+\mathit{\_}\mathit{a})}^{-1}d\mathit{\_}\mathit{a}+\ln (x+a)+\mathit{\_}\mathit{C}\mathit{1})(x+a)\}$$