#### 2.484   ODE No. 484

$\left (2 x y(x)-x^2\right ) y'(x)^2-6 x y(x) y'(x)-y(x)^2+2 x y(x)=0$ Mathematica : cpu = 0.162016 (sec), leaf count = 81

$\left \{\left \{y(x)\to -\sqrt {3 x^2-2 e^{\frac {c_1}{2}} x}+2 x-e^{\frac {c_1}{2}}\right \},\left \{y(x)\to \sqrt {3 x^2-2 e^{\frac {c_1}{2}} x}+2 x-e^{\frac {c_1}{2}}\right \}\right \}$ Maple : cpu = 0.051 (sec), leaf count = 115

$\left \{ y \left ( x \right ) =0,y \left ( x \right ) ={\it RootOf} \left ( -2\,\ln \left ( x \right ) +\int ^{{\it \_Z}}\!{\frac {1}{{\it \_a}\, \left ( {{\it \_a}}^{2}-4\,{\it \_a}+1 \right ) } \left ( -2\,{{\it \_a}}^{2}+\sqrt {2}\sqrt {{\it \_a}\, \left ( {\it \_a}+1 \right ) ^{2}}+4\,{\it \_a} \right ) }{d{\it \_a}}+2\,{\it \_C1} \right ) x,y \left ( x \right ) ={\it RootOf} \left ( -2\,\ln \left ( x \right ) -\int ^{{\it \_Z}}\!{\frac {1}{{\it \_a}\, \left ( {{\it \_a}}^{2}-4\,{\it \_a}+1 \right ) } \left ( 2\,{{\it \_a}}^{2}+\sqrt {2}\sqrt {{\it \_a}\, \left ( {\it \_a}+1 \right ) ^{2}}-4\,{\it \_a} \right ) }{d{\it \_a}}+2\,{\it \_C1} \right ) x \right \}$