2.321   ODE No. 321

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

\[ \left (2 \text {Global$\grave { }$x}^2 \text {Global$\grave { }$y}(\text {Global$\grave { }$x})^3+\text {Global$\grave { }$x}^2 \text {Global$\grave { }$y}(\text {Global$\grave { }$x})^2-2 \text {Global$\grave { }$x}\right ) \text {Global$\grave { }$y}'(\text {Global$\grave { }$x})-2 \text {Global$\grave { }$y}(\text {Global$\grave { }$x})-1=0 \] Mathematica : cpu = 0.182267 (sec), leaf count = 47

\[\text {Solve}\left [\frac {1}{64} \left (-4 \text {Global$\grave { }$y}(\text {Global$\grave { }$x})^2+4 \text {Global$\grave { }$y}(\text {Global$\grave { }$x})-2 \log (8 \text {Global$\grave { }$y}(\text {Global$\grave { }$x})+4)+3\right )-\frac {1}{4 \text {Global$\grave { }$x} (2 \text {Global$\grave { }$y}(\text {Global$\grave { }$x})+1)}=c_1,\text {Global$\grave { }$y}(\text {Global$\grave { }$x})\right ]\]

Maple : cpu = 0.171 (sec), leaf count = 42

\[ \left \{ y \left ( x \right ) ={\frac {{{\rm e}^{{\it RootOf} \left ( x \left ( {{\rm e}^{{\it \_Z}}} \right ) ^{3}-4\,x \left ( {{\rm e}^{{\it \_Z}}} \right ) ^{2}+8\,{\it \_C1}\,x{{\rm e}^{{\it \_Z}}}+2\,{\it \_Z}\,x{{\rm e}^{{\it \_Z}}}+3\,x{{\rm e}^{{\it \_Z}}}+16 \right ) }}}{2}}-{\frac {1}{2}} \right \} \]