\[ y'(x)=\frac {x F((y(x)-x) (y(x)+x))}{y(x)} \] ✓ 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]
\[\text {Solve}\left [\int _1^{y(x)}\left (\frac {K[2]}{F((K[2]-x) (x+K[2]))-1}-\int _1^x\left (\frac {2 F((K[2]-K[1]) (K[1]+K[2])) K[1] K[2] F'((K[2]-K[1]) (K[1]+K[2]))}{(F((K[2]-K[1]) (K[1]+K[2]))-1)^2}-\frac {2 K[1] K[2] F'((K[2]-K[1]) (K[1]+K[2]))}{F((K[2]-K[1]) (K[1]+K[2]))-1}\right )dK[1]\right )dK[2]+\int _1^x-\frac {F((y(x)-K[1]) (K[1]+y(x))) K[1]}{F((y(x)-K[1]) (K[1]+y(x)))-1}dK[1]=c_1,y(x)\right ]\] ✓ 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))
\[y \left (x \right ) = \sqrt {x^{2}+\RootOf \left (-x^{2}+\int _{}^{\textit {\_Z}}\frac {1}{F \left (\textit {\_a} \right )-1}d \textit {\_a} +2 c_{1}\right )}\]