ODE No. 849

$$y^{\prime }(x)=x^2\sqrt{x^2+4y(x)-4x}+\sqrt{x^2+4y(x)-4x}+x^3\sqrt{x^2+4y(x)-4x}-\frac{x}{2}+1$$ ✓ Mathematica : cpu = 1.02817 (sec), leaf count = 102

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

$$\text{Solve}[\frac{x^4}{4}+\frac{x^3}{3}-\frac{1}{2}\sqrt{x^2+4y(x)-4x}+\log (-\sqrt{x^2+4y(x)-4x}-x+2)-{\tanh }^{-1}\left(\frac{2x-4}{2\sqrt{x^2+4y(x)-4x}}\right)-\frac{1}{2}\log (2-2y(x))+x=c_1,y(x)]$$ ✓ Maple : cpu = 0.333 (sec), leaf count = 33

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

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