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 = 0.159791 (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 = 0.578 (sec), leaf count = 203


\[y \relax (x ) = -\frac {\sqrt {3}\, x}{3}\]