\[ \boxed { 3\, \left ( y \left ( x \right ) \right ) ^{2} \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}-2\,xy \left ( x \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +4\, \left ( y \left ( x \right ) \right ) ^{2}-{x}^{2}=0} \]
Mathematica: cpu = 0.174022 (sec), leaf count = 203 \[ \left \{\left \{y(x)\to -\frac {\sqrt {-4 i x \sinh \left (3 c_1\right )-4 i x \cosh \left (3 c_1\right )+\sinh \left (6 c_1\right )+\cosh \left (6 c_1\right )-3 x^2}}{\sqrt {3}}\right \},\left \{y(x)\to \frac {\sqrt {-4 i x \sinh \left (3 c_1\right )-4 i x \cosh \left (3 c_1\right )+\sinh \left (6 c_1\right )+\cosh \left (6 c_1\right )-3 x^2}}{\sqrt {3}}\right \},\left \{y(x)\to -\frac {\sqrt {4 i x \sinh \left (3 c_1\right )+4 i x \cosh \left (3 c_1\right )+\sinh \left (6 c_1\right )+\cosh \left (6 c_1\right )-3 x^2}}{\sqrt {3}}\right \},\left \{y(x)\to \frac {\sqrt {4 i x \sinh \left (3 c_1\right )+4 i x \cosh \left (3 c_1\right )+\sinh \left (6 c_1\right )+\cosh \left (6 c_1\right )-3 x^2}}{\sqrt {3}}\right \}\right \} \]
Maple: cpu = 0.889 (sec), leaf count = 203 \[ \left \{ \ln \left ( x \right ) -{\frac {\sqrt {3}}{6}\sqrt {{\frac { \left ( \sqrt {3}x-3\,y \left ( x \right ) \right ) \left ( \sqrt {3}x+3 \,y \left ( x \right ) \right ) }{{x}^{2}}}}}+{\frac {1}{2}\sqrt {{ \frac {{x}^{2}-3\, \left ( y \left ( x \right ) \right ) ^{2}}{{x}^{2}}}} }-{\it Artanh} \left ( {\frac {1}{2}\sqrt {{\frac {{x}^{2}-3\, \left ( y \left ( x \right ) \right ) ^{2}}{{x}^{2}}}}} \right ) +{\frac {1}{2} \ln \left ( {\frac { \left ( y \left ( x \right ) \right ) ^{2}+{x}^{2}}{ {x}^{2}}} \right ) }-{\it \_C1}=0,\ln \left ( x \right ) +{\frac {\sqrt {3}}{6}\sqrt {{\frac { \left ( \sqrt {3}x-3\,y \left ( x \right ) \right ) \left ( \sqrt {3}x+3\,y \left ( x \right ) \right ) }{{x}^{2}}} }}-{\frac {1}{2}\sqrt {{\frac {{x}^{2}-3\, \left ( y \left ( x \right ) \right ) ^{2}}{{x}^{2}}}}}+{\it Artanh} \left ( {\frac {1}{2}\sqrt {{ \frac {{x}^{2}-3\, \left ( y \left ( x \right ) \right ) ^{2}}{{x}^{2}}}} } \right ) +{\frac {1}{2}\ln \left ( {\frac { \left ( y \left ( x \right ) \right ) ^{2}+{x}^{2}}{{x}^{2}}} \right ) }-{\it \_C1}=0,y \left ( x \right ) =-{\frac {\sqrt {3}x}{3}},y \left ( x \right ) ={ \frac {\sqrt {3}x}{3}} \right \} \]