2.351   ODE No. 351

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

\[ \text {Global$\grave { }$y}'(\text {Global$\grave { }$x}) \cos (\text {Global$\grave { }$y}(\text {Global$\grave { }$x}))-\sin ^3(\text {Global$\grave { }$y}(\text {Global$\grave { }$x}))+\text {Global$\grave { }$x} \sin (\text {Global$\grave { }$y}(\text {Global$\grave { }$x})) \cos ^2(\text {Global$\grave { }$y}(\text {Global$\grave { }$x}))=0 \] Mathematica : cpu = 0.366627 (sec), leaf count = 61

\[\left \{\left \{\text {Global$\grave { }$y}(\text {Global$\grave { }$x})\to -\cot ^{-1}\left (\sqrt {e^{\text {Global$\grave { }$x}^2} \left (4 c_1-\sqrt {\pi } \text {erf}(\text {Global$\grave { }$x})\right )}\right )\right \},\left \{\text {Global$\grave { }$y}(\text {Global$\grave { }$x})\to \cot ^{-1}\left (\sqrt {e^{\text {Global$\grave { }$x}^2} \left (4 c_1-\sqrt {\pi } \text {erf}(\text {Global$\grave { }$x})\right )}\right )\right \}\right \}\]

Maple : cpu = 0.515 (sec), leaf count = 55

\[ \left \{ y \left ( x \right ) =-\arcsin \left ( {\frac {1}{\sqrt {1-\sqrt {\pi }{\it Erf} \left ( x \right ) {{\rm e}^{{x}^{2}}}-2\,{\it \_C1}\,{{\rm e}^{{x}^{2}}}}}} \right ) ,y \left ( x \right ) =\arcsin \left ( {\frac {1}{\sqrt {1-\sqrt {\pi }{\it Erf} \left ( x \right ) {{\rm e}^{{x}^{2}}}-2\,{\it \_C1}\,{{\rm e}^{{x}^{2}}}}}} \right ) \right \} \]