ODE No. 601

$$y^{\prime }(x)=\frac{xF((y(x)-x)(y(x)+x))}{y(x)}$$ ✓ Mathematica : cpu = 0.255247 (sec), leaf count = 182

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

$$\text{Solve}[{\int }_1^{y(x)}(\frac{K[2]}{F((K[2]-x)(x+K[2]))-1}-{\int }_1^x(\frac{2F((K[2]-K[1])(K[1]+K[2]))K[1]K[2]F^{\prime }((K[2]-K[1])(K[1]+K[2]))}{(F((K[2]-K[1])(K[1]+K[2]))-1{)}^2}-\frac{2K[1]K[2]F^{\prime }((K[2]-K[1])(K[1]+K[2]))}{F((K[2]-K[1])(K[1]+K[2]))-1})dK[1])dK[2]+{\int }_1^x-\frac{F((y(x)-K[1])(K[1]+y(x)))K[1]}{F((y(x)-K[1])(K[1]+y(x)))-1}dK[1]=c_1,y(x)]$$ ✓ Maple : cpu = 0.13 (sec), leaf count = 61

dsolve(diff(y(x),x) = F(-(x-y(x))*(y(x)+x))*x/y(x),y(x))
 

$$y\left(x\right)=\sqrt{x^2+\mathrm{RootOf}(-x^2+{\int }_{}^{\mathit{\text{\_Z}}}\frac{1}{F\left(\mathit{\text{\_a}}\right)-1}d\mathit{\text{\_a}}+2c_1)}$$