#### 2.166   ODE No. 166

$2 (x-1) x y'(x)+(x-1) y(x)^2-x=0$ Mathematica : cpu = 0.140976 (sec), leaf count = 71

$\left \{\left \{y(x)\to \frac {2 x \left (\frac {c_1 (E(x)-K(x))}{\pi x}-G_{2,2}^{2,0}\left (x\left |\begin {array}{c} -\frac {1}{2},\frac {1}{2} \\ -1,0 \\\end {array}\right .\right )\right )}{G_{2,2}^{2,0}\left (x\left |\begin {array}{c} \frac {1}{2},\frac {3}{2} \\ 0,0 \\\end {array}\right .\right )+\frac {2 c_1 E(x)}{\pi }}\right \}\right \}$ Maple : cpu = 0.118 (sec), leaf count = 97

$\left \{ y \left ( x \right ) ={\frac {x}{2\,x-2} \left ( {\it LegendreQ} \left ( -{\frac {1}{2}},1,{\frac {2-x}{x}} \right ) {\it \_C1}-{\it LegendreQ} \left ( {\frac {1}{2}},1,{\frac {2-x}{x}} \right ) {\it \_C1}+{\it LegendreP} \left ( -{\frac {1}{2}},1,{\frac {2-x}{x}} \right ) -{\it LegendreP} \left ( {\frac {1}{2}},1,{\frac {2-x}{x}} \right ) \right ) \left ( {\it LegendreQ} \left ( -{\frac {1}{2}},1,{\frac {2-x}{x}} \right ) {\it \_C1}+{\it LegendreP} \left ( -{\frac {1}{2}},1,{\frac {2-x}{x}} \right ) \right ) ^{-1}} \right \}$