#### 2.497   ODE No. 497

$-x^2-2 x y(x) y'(x)+3 y(x)^2 y'(x)^2+4 y(x)^2=0$ Mathematica : cpu = 0.158235 (sec), leaf count = 76

$\left \{\left \{y(x)\to -\frac {\sqrt {-3 x^2-4 i e^{3 c_1} x+e^{6 c_1}}}{\sqrt {3}}\right \},\left \{y(x)\to \frac {\sqrt {-3 x^2-4 i e^{3 c_1} x+e^{6 c_1}}}{\sqrt {3}}\right \}\right \}$ Maple : cpu = 0.722 (sec), leaf count = 203

$\left \{ \ln \left ( x \right ) -{\frac {\sqrt {3}}{6}\sqrt {{\frac { \left ( \sqrt {3}x+3\,y \left ( x \right ) \right ) \left ( \sqrt {3}x-3\,y \left ( x \right ) \right ) }{{x}^{2}}}}}+{\frac {1}{2}\sqrt {{\frac {{x}^{2}-3\, \left ( y \left ( x \right ) \right ) ^{2}}{{x}^{2}}}}}-{\it Artanh} \left ( {\frac {1}{2}\sqrt {{\frac {{x}^{2}-3\, \left ( y \left ( x \right ) \right ) ^{2}}{{x}^{2}}}}} \right ) +{\frac {1}{2}\ln \left ( {\frac { \left ( y \left ( x \right ) \right ) ^{2}+{x}^{2}}{{x}^{2}}} \right ) }-{\it \_C1}=0,\ln \left ( x \right ) +{\frac {\sqrt {3}}{6}\sqrt {{\frac { \left ( \sqrt {3}x+3\,y \left ( x \right ) \right ) \left ( \sqrt {3}x-3\,y \left ( x \right ) \right ) }{{x}^{2}}}}}-{\frac {1}{2}\sqrt {{\frac {{x}^{2}-3\, \left ( y \left ( x \right ) \right ) ^{2}}{{x}^{2}}}}}+{\it Artanh} \left ( {\frac {1}{2}\sqrt {{\frac {{x}^{2}-3\, \left ( y \left ( x \right ) \right ) ^{2}}{{x}^{2}}}}} \right ) +{\frac {1}{2}\ln \left ( {\frac { \left ( y \left ( x \right ) \right ) ^{2}+{x}^{2}}{{x}^{2}}} \right ) }-{\it \_C1}=0,y \left ( x \right ) =-{\frac {\sqrt {3}x}{3}},y \left ( x \right ) ={\frac {\sqrt {3}x}{3}} \right \}$