2.321   ODE No. 321

  1. Problem in Latex
  2. Mathematica input
  3. Maple input

\[ \left (2 x^2 y(x)^3+x^2 y(x)^2-2 x\right ) y'(x)-2 y(x)-1=0 \] Mathematica : cpu = 0.525617 (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 = 0.231 (sec), leaf count = 42

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