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 = 0.28043 (sec), leaf count = 47

DSolve[-1 - 2*y[x] + (-2*x + x^2*y[x]^2 + 2*x^2*y[x]^3)*Derivative[1][y][x] == 0,y[x],x]
 

\[\text {Solve}\left [\frac {1}{64} \left (-4 y(x)^2+4 y(x)-2 \log (8 y(x)+4)+3\right )-\frac {1}{4 x (2 y(x)+1)}=c_1,y(x)\right ]\] Maple : cpu = 0.114 (sec), leaf count = 42

dsolve((2*x^2*y(x)^3+y(x)^2*x^2-2*x)*diff(y(x),x)-2*y(x)-1 = 0,y(x))
 

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