2.242   ODE No. 242

\[ 2 x y(x) y'(x)+2 y(x)^2+1=0 \] Mathematica : cpu = 0.0835599 (sec), leaf count = 60


\[\left \{\left \{y(x)\to -\frac {\sqrt {-x^2+e^{4 c_1}}}{\sqrt {2} x}\right \},\left \{y(x)\to \frac {\sqrt {-x^2+e^{4 c_1}}}{\sqrt {2} x}\right \}\right \}\] Maple : cpu = 0.021 (sec), leaf count = 39


\[y \relax (x ) = -\frac {\sqrt {-2 x^{2}+4 c_{1}}}{2 x}\]