ODE No. 577

$$y^{\prime }(x)=F\left(\frac{y(x)}{a+x}\right)$$ ✓ Mathematica : cpu = 0.271736 (sec), leaf count = 243

DSolve[Derivative[1][y][x] == F[y[x]/(a + x)],y[x],x]
 

$$\text{Solve}[{\int }_1^{y(x)}(\frac{1}{-aF\left(\frac{K[2]}{a+x}\right)-xF\left(\frac{K[2]}{a+x}\right)+K[2]}-{\int }_1^x(\frac{F^{\prime }\left(\frac{K[2]}{a+K[1]}\right)}{(a+K[1])(aF\left(\frac{K[2]}{a+K[1]}\right)+K[1]F\left(\frac{K[2]}{a+K[1]}\right)-K[2])}-\frac{F\left(\frac{K[2]}{a+K[1]}\right)(\frac{a{F}^{\prime }\left(\frac{K[2]}{a+K[1]}\right)}{a+K[1]}+\frac{K[1]F^{\prime }\left(\frac{K[2]}{a+K[1]}\right)}{a+K[1]}-1)}{{(aF\left(\frac{K[2]}{a+K[1]}\right)+K[1]F\left(\frac{K[2]}{a+K[1]}\right)-K[2])}^2})dK[1])dK[2]+{\int }_1^x\frac{F\left(\frac{y(x)}{a+K[1]}\right)}{aF\left(\frac{y(x)}{a+K[1]}\right)+K[1]F\left(\frac{y(x)}{a+K[1]}\right)-y(x)}dK[1]=c_1,y(x)]$$ ✓ Maple : cpu = 0.038 (sec), leaf count = 28

dsolve(diff(y(x),x) = F(y(x)/(x+a)),y(x))
 

$$y\left(x\right)=-\mathrm{RootOf}({\int }_{}^{\mathit{\text{\_Z}}}\frac{1}{F(-\mathit{\text{\_a}})+\mathit{\text{\_a}}}d\mathit{\text{\_a}}+\ln (x+a)+c_1)(x+a)$$