3.351   ODE No. 351

\[ \boxed { \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) \cos \left ( y \left ( x \right ) \right ) +x\sin \left ( y \left ( x \right ) \right ) \left ( \cos \left ( y \left ( x \right ) \right ) \right ) ^{2}- \left ( \sin \left ( y \left ( x \right ) \right ) \right ) ^{3}=0} \]

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

Mathematica: cpu = 0.367047 (sec), leaf count = 61 \[ \left \{\left \{y(x)\to -\cot ^{-1}\left (\sqrt {e^{x^2} \left (4 c_1-\sqrt {\pi } \text {erf}(x)\right )}\right )\right \},\left \{y(x)\to \cot ^{-1}\left (\sqrt {e^{x^2} \left (4 c_1-\sqrt {\pi } \text {erf}(x)\right )}\right )\right \}\right \} \]

Maple: cpu = 0.343 (sec), leaf count = 55 \[ \left \{ y \left ( x \right ) =-\arcsin \left ( {\frac {1}{\sqrt {1- \sqrt {\pi }{\it Erf} \left ( x \right ) {{\rm e}^{{x}^{2}}}-2\,{\it \_C1}\,{{\rm e}^{{x}^{2}}}}}} \right ) ,y \left ( x \right ) =\arcsin \left ( {\frac {1}{\sqrt {1-\sqrt {\pi }{\it Erf} \left ( x \right ) { {\rm e}^{{x}^{2}}}-2\,{\it \_C1}\,{{\rm e}^{{x}^{2}}}}}} \right ) \right \} \]