ODE No. 607

$$y^{\prime }(x)=\frac{x^{3}F\left(\frac{y(x)}{x^2}\right)+2y(x)}{x}$$ ✓ Mathematica : cpu = 0.233257 (sec), leaf count = 121

DSolve[Derivative[1][y][x] == (x^3*F[y[x]/x^2] + 2*y[x])/x,y[x],x]
 

$$\text{Solve}[{\int }_1^{y(x)}-\frac{F\left(\frac{K[2]}{x^2}\right){\int }_1^x(\frac{2}{F\left(\frac{K[2]}{K[1{]}^2}\right)K[1{]}^3}-\frac{2K[2]F^{\prime }\left(\frac{K[2]}{K[1{]}^2}\right)}{F{\left(\frac{K[2]}{K[1{]}^2}\right)}^{2}K[1{]}^5})dK[1]x^2+1}{x^{2}F\left(\frac{K[2]}{x^2}\right)}dK[2]+{\int }_1^x(\frac{2y(x)}{F\left(\frac{y(x)}{K[1{]}^2}\right)K[1{]}^3}+1)dK[1]=c_1,y(x)]$$ ✓ Maple : cpu = 0.11 (sec), leaf count = 22

dsolve(diff(y(x),x) = (2*y(x)+F(1/x^2*y(x))*x^3)/x,y(x))
 

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