ODE No. 649

\[ y'(x)=x \sqrt {x^2+8 y(x)-2 x+1}-\frac {x}{4}+\frac {1}{4} \]

✓ Mathematica : cpu = 0.248724 (sec), leaf count = 37

DSolve[Derivative[1][y][x] == 1/4 - x/4 + x*Sqrt[1 - 2*x + x^2 + 8*y[x]],y[x],x]

\[\left \{\left \{y(x)\to \frac {1}{8} \left (4 x^4-x^2-16 c_1 x^2+2 x-1+16 c_1{}^2\right )\right \}\right \}\]

✓ Maple : cpu = 0.291 (sec), leaf count = 27

dsolve(diff(y(x),x) = -1/4*x+1/4+x*(x^2-2*x+1+8*y(x))^(1/2),y(x))

\[c_{1} +\frac {x^{2}}{8}+\frac {17}{128}-\frac {\sqrt {x^{2}-2 x +1+8 y \left (x \right )}}{16} = 0\]