2.588   ODE No. 588

\[ y'(x)=\frac {F((y(x)-x) (y(x)+x))+x}{y(x)} \]

✓ Mathematica : cpu = 0.203253 (sec), leaf count = 109

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

\[\text {Solve}\left [\int _1^{y(x)}\left (-\frac {K[2]}{F((K[2]-x) (x+K[2]))}-\int _1^x-\frac {2 K[1] K[2] F'((K[2]-K[1]) (K[1]+K[2]))}{F((K[2]-K[1]) (K[1]+K[2]))^2}dK[1]\right )dK[2]+\int _1^x\left (\frac {K[1]}{F((y(x)-K[1]) (K[1]+y(x)))}+1\right )dK[1]=c_1,y(x)\right ]\]

✓ Maple : cpu = 0.143 (sec), leaf count = 53

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

\[y \left (x \right ) = \sqrt {x^{2}+\operatorname {RootOf}\left (-2 x +\int _{}^{\textit {\_Z}}\frac {1}{F \left (\textit {\_a} \right )}d \textit {\_a} +2 c_{1} \right )}\]