2.251   ODE No. 251

\[ \left (x^2 y(x)-1\right ) y'(x)+x y(x)^2-1=0 \] Mathematica : cpu = 0.138568 (sec), leaf count = 60


\[\left \{\left \{y(x)\to \frac {1}{x^2}-\frac {\sqrt {2 x^3+c_1 x^2+1}}{x^2}\right \},\left \{y(x)\to \frac {1}{x^2}+\frac {\sqrt {2 x^3+c_1 x^2+1}}{x^2}\right \}\right \}\] Maple : cpu = 0.017 (sec), leaf count = 51


\[y \relax (x ) = \frac {1+\sqrt {2 x^{3}-2 x^{2} c_{1}+1}}{x^{2}}\]