2.715   ODE No. 715

\[ y'(x)=\frac {-\frac {x^2}{2}+x^3 \sqrt {x^2+4 y(x)-4 x}+\frac {x}{2}+1}{x+1} \]

✓ Mathematica : cpu = 0.618674 (sec), leaf count = 50

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

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

✓ Maple : cpu = 0.331 (sec), leaf count = 39

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

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