ODE No. 662

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

✓ Mathematica : cpu = 0.311375 (sec), leaf count = 37

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

\[\left \{\left \{y(x)\to \frac {1}{36} \left (-4 x^6+24 c_1 x^3+9 x^2+18 x+9-36 c_1{}^2\right )\right \}\right \}\]

✓ Maple : cpu = 0.288 (sec), leaf count = 26

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

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