#### 2.540   ODE No. 540

$2 y(x) y'(x)^3-y(x) y'(x)^2+2 x y'(x)-x=0$ Mathematica : cpu = 0.0291333 (sec), leaf count = 69

$\left \{\left \{y(x)\to \frac {x}{2}+c_1\right \},\left \{y(x)\to \frac {\left (3 c_1-2 i x^{3/2}\right ){}^{2/3}}{2^{2/3}}\right \},\left \{y(x)\to \frac {\left (2 i x^{3/2}+3 c_1\right ){}^{2/3}}{2^{2/3}}\right \}\right \}$ Maple : cpu = 0.164 (sec), leaf count = 109

$\left \{ x+{\frac {{\it \_C1}\,x}{y \left ( x \right ) } \left ( {\frac {1}{y \left ( x \right ) } \left ( -x-\sqrt {-xy \left ( x \right ) }+y \left ( x \right ) \right ) } \right ) ^{-{\frac {2}{3}}} \left ( {\frac {1}{y \left ( x \right ) } \left ( \sqrt {-xy \left ( x \right ) }+y \left ( x \right ) \right ) } \right ) ^{-{\frac {2}{3}}}}=0,x+{\frac {{\it \_C1}\,x}{y \left ( x \right ) } \left ( {\frac {1}{y \left ( x \right ) } \left ( -x+\sqrt {-xy \left ( x \right ) }+y \left ( x \right ) \right ) } \right ) ^{-{\frac {2}{3}}} \left ( {\frac {1}{y \left ( x \right ) } \left ( -\sqrt {-xy \left ( x \right ) }+y \left ( x \right ) \right ) } \right ) ^{-{\frac {2}{3}}}}=0,y \left ( x \right ) ={\frac {x}{2}}+{\it \_C1} \right \}$