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 = 0.329998 (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 = 0.143 (sec), leaf count = 42

\[ \left \{ y \left ( x \right ) ={\frac {{{\rm e}^{{\it RootOf} \left ( x \left ( {{\rm e}^{{\it \_Z}}} \right ) ^{3}-4\,x \left ( {{\rm e}^{{\it \_Z}}} \right ) ^{2}+16\,{\it \_C1}\,x{{\rm e}^{{\it \_Z}}}+2\,{\it \_Z}\,x{{\rm e}^{{\it \_Z}}}+3\,x{{\rm e}^{{\it \_Z}}}+16 \right ) }}}{2}}-{\frac {1}{2}} \right \} \]