ODE No. 650

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

✓ Mathematica : cpu = 0.301151 (sec), leaf count = 40

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

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

✓ Maple : cpu = 0.331 (sec), leaf count = 35

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

\[c_{1} +\frac {a^{2}}{4}+\frac {x^{2}}{4}+\frac {1}{16}-\frac {\sqrt {x^{2}+2 a x +a^{2}+4 y \left (x \right )}}{4} = 0\]