#### 2.466   ODE No. 466

$y(x) y'(x)^2-2 x y'(x)+y(x)=0$ Mathematica : cpu = 1.87605 (sec), leaf count = 433

$\left \{\text {Solve}\left [-\frac {i \sqrt {\frac {y(x)^2}{x^2}-1} \tan ^{-1}\left (\sqrt {\frac {y(x)^2}{x^2}-1}\right )}{\sqrt {\frac {y(x)}{x}-1} \sqrt {\frac {y(x)}{x}+1}}-i \sqrt {\frac {\frac {y(x)}{x}-1}{\frac {y(x)}{x}+1}} \left (\frac {y(x)}{x}+1\right )+i \sqrt {\frac {y(x)}{x}-1} \sqrt {\frac {y(x)}{x}+1}+\log \left (\frac {y(x)}{x}\right )+\frac {2 i \sqrt {\frac {y(x)}{x}-1} \sin ^{-1}\left (\frac {\sqrt {1-\frac {y(x)}{x}}}{\sqrt {2}}\right )}{\sqrt {1-\frac {y(x)}{x}}}-2 i \tanh ^{-1}\left (\sqrt {\frac {\frac {y(x)}{x}-1}{\frac {y(x)}{x}+1}}\right )=c_1-\log (x),y(x)\right ],\text {Solve}\left [\frac {i \sqrt {\frac {y(x)^2}{x^2}-1} \tan ^{-1}\left (\sqrt {\frac {y(x)^2}{x^2}-1}\right )}{\sqrt {\frac {y(x)}{x}-1} \sqrt {\frac {y(x)}{x}+1}}+i \sqrt {\frac {\frac {y(x)}{x}-1}{\frac {y(x)}{x}+1}} \left (\frac {y(x)}{x}+1\right )-i \sqrt {\frac {y(x)}{x}-1} \sqrt {\frac {y(x)}{x}+1}+\log \left (\frac {y(x)}{x}\right )-\frac {2 i \sqrt {\frac {y(x)}{x}-1} \sin ^{-1}\left (\frac {\sqrt {1-\frac {y(x)}{x}}}{\sqrt {2}}\right )}{\sqrt {1-\frac {y(x)}{x}}}+2 i \tanh ^{-1}\left (\sqrt {\frac {\frac {y(x)}{x}-1}{\frac {y(x)}{x}+1}}\right )=c_1-\log (x),y(x)\right ]\right \}$ Maple : cpu = 1.201 (sec), leaf count = 71

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