ODE No. 641

$$y^{\prime }(x)=\frac{x^4\sqrt{4x^{2}y(x)+1}+\frac{1}{2}}{x^3}$$ ✓ Mathematica : cpu = 0.214723 (sec), leaf count = 35

DSolve[Derivative[1][y][x] == (1/2 + x^4*Sqrt[1 + 4*x^2*y[x]])/x^3,y[x],x]
 

$$\left\{\{y(x)\to \frac{4x^8-24c_1{x}^5+36c_1{}^2{x}^2-9}{36x^2}\}\right\}$$ ✓ Maple : cpu = 0.364 (sec), leaf count = 26

dsolve(diff(y(x),x) = 1/2*(1+2*(4*x^2*y(x)+1)^(1/2)*x^4)/x^3,y(x))
 

$$c_1-\frac{\sqrt{4x^{2}y\left(x\right)+1}}{x}+\frac{2x^3}{3}=0$$