#### 2.456   ODE No. 456

$2 \left (1-x^2\right ) y(x) y'(x)+x \left (x^2-1\right ) y'(x)^2+x y(x)^2-x=0$ Mathematica : cpu = 0.123681 (sec), leaf count = 421

$\left \{\left \{y(x)\to \frac {-x-x \tanh ^2\left (\frac {1}{4} \left (2 c_1-\frac {i \sqrt {x-1} \sqrt {x+1} \sqrt {(x-1) (x+1)} \tan ^{-1}\left (\sqrt {x^2-1}\right )}{1-x}-\frac {i \sqrt {x-1} \sqrt {(x-1) (x+1)} \tan ^{-1}\left (\sqrt {x^2-1}\right )}{\sqrt {x+1}}\right )\right )}{-1+\tanh ^2\left (\frac {1}{4} \left (2 c_1-\frac {i \sqrt {x-1} \sqrt {x+1} \sqrt {(x-1) (x+1)} \tan ^{-1}\left (\sqrt {x^2-1}\right )}{1-x}-\frac {i \sqrt {x-1} \sqrt {(x-1) (x+1)} \tan ^{-1}\left (\sqrt {x^2-1}\right )}{\sqrt {x+1}}\right )\right )}\right \},\left \{y(x)\to \frac {-x-x \tanh ^2\left (\frac {1}{4} \left (2 c_1+\frac {i \sqrt {x-1} \sqrt {x+1} \sqrt {(x-1) (x+1)} \tan ^{-1}\left (\sqrt {x^2-1}\right )}{1-x}+\frac {i \sqrt {x-1} \sqrt {(x-1) (x+1)} \tan ^{-1}\left (\sqrt {x^2-1}\right )}{\sqrt {x+1}}\right )\right )}{-1+\tanh ^2\left (\frac {1}{4} \left (2 c_1+\frac {i \sqrt {x-1} \sqrt {x+1} \sqrt {(x-1) (x+1)} \tan ^{-1}\left (\sqrt {x^2-1}\right )}{1-x}+\frac {i \sqrt {x-1} \sqrt {(x-1) (x+1)} \tan ^{-1}\left (\sqrt {x^2-1}\right )}{\sqrt {x+1}}\right )\right )}\right \}\right \}$ Maple : cpu = 0.72 (sec), leaf count = 33

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