#### 2.474   ODE No. 474

$2 y(x) y'(x)^2-(4 x-5) y'(x)+2 y(x)=0$ Mathematica : cpu = 0.160649 (sec), leaf count = 135

$\left \{\left \{y(x)\to -i \sqrt {2} e^{\frac {c_1}{2}} \sqrt {4 x-5+8 e^{c_1}}\right \},\left \{y(x)\to i \sqrt {2} e^{\frac {c_1}{2}} \sqrt {4 x-5+8 e^{c_1}}\right \},\left \{y(x)\to -\frac {1}{4} i e^{\frac {c_1}{2}} \sqrt {8 x-10+e^{c_1}}\right \},\left \{y(x)\to \frac {1}{4} i e^{\frac {c_1}{2}} \sqrt {8 x-10+e^{c_1}}\right \}\right \}$ Maple : cpu = 1.702 (sec), leaf count = 152

$\left \{ \ln \left ( x-{\frac {5}{4}} \right ) -{\frac {1}{2}\ln \left ( 4\,{\frac {y \left ( x \right ) }{4\,x-5}}-1 \right ) }-{\frac {1}{2}\ln \left ( 4\,{\frac {y \left ( x \right ) }{4\,x-5}}+1 \right ) }+\ln \left ( {\frac {y \left ( x \right ) }{4\,x-5}} \right ) +{\frac {1}{2}\ln \left ( 16\,{\frac { \left ( y \left ( x \right ) \right ) ^{2}}{ \left ( 4\,x-5 \right ) ^{2}}}-1 \right ) }+{\frac {\sqrt {4}}{2}\sqrt {{\frac {1}{ \left ( 4\,x-5 \right ) ^{2}} \left ( -16\, \left ( y \left ( x \right ) \right ) ^{2}+16\, \left ( x-5/4 \right ) ^{2} \right ) }}}-\sqrt {-16\,{\frac { \left ( y \left ( x \right ) \right ) ^{2}}{ \left ( 4\,x-5 \right ) ^{2}}}+1}+{\it Artanh} \left ( {\frac {1}{\sqrt {-16\,{\frac { \left ( y \left ( x \right ) \right ) ^{2}}{ \left ( 4\,x-5 \right ) ^{2}}}+1}}} \right ) -{\it \_C1}=0,y \left ( x \right ) =-x+{\frac {5}{4}},y \left ( x \right ) =x-{\frac {5}{4}} \right \}$