2.610   ODE No. 610

\[ y'(x)=\frac {x^2 F\left (\frac {y(x)}{x}\right )+y(x)}{x} \]

✓ Mathematica : cpu = 0.072971 (sec), leaf count = 25

DSolve[Derivative[1][y][x] == (x^2*F[y[x]/x] + y[x])/x,y[x],x]
 

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

✓ Maple : cpu = 0.014 (sec), leaf count = 20

dsolve(diff(y(x),x) = (y(x)+F(y(x)/x)*x^2)/x,y(x))
 

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