2.321   ODE No. 321

\[ \left (2 x^2 y(x)^3+x^2 y(x)^2-2 x\right ) y'(x)-2 y(x)-1=0 \] Mathematica : cpu = 0.452487 (sec), leaf count = 47


\[\text {Solve}\left [\frac {1}{64} \left (-4 y(x)^2+4 y(x)-2 \log (8 y(x)+4)+3\right )-\frac {1}{4 x (2 y(x)+1)}=c_1,y(x)\right ]\] Maple : cpu = 0.254 (sec), leaf count = 42


\[y \relax (x ) = \frac {{\mathrm e}^{\RootOf \left (x \,{\mathrm e}^{3 \textit {\_Z}}-4 x \,{\mathrm e}^{2 \textit {\_Z}}+8 c_{1} x \,{\mathrm e}^{\textit {\_Z}}+2 \textit {\_Z} x \,{\mathrm e}^{\textit {\_Z}}+3 x \,{\mathrm e}^{\textit {\_Z}}+16\right )}}{2}-\frac {1}{2}\]