ODE No. 664

\[ y'(x)=x^2 \sqrt {x^2+4 y(x)-4 x}-\frac {x}{2}+1 \]

✓ Mathematica : cpu = 0.148577 (sec), leaf count = 36

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

\[\left \{\left \{y(x)\to \frac {1}{36} \left (4 x^6-24 c_1 x^3-9 x^2+36 x+36 c_1{}^2\right )\right \}\right \}\]

✓ Maple : cpu = 0.233 (sec), leaf count = 25

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

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