2.351   ODE No. 351

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

\[ y'(x) \cos (y(x))-\sin ^3(y(x))+x \sin (y(x)) \cos ^2(y(x))=0 \] Mathematica : cpu = 0.467968 (sec), leaf count = 61

\[\left \{\left \{y(x)\to -\cot ^{-1}\left (\sqrt {e^{x^2} \left (-\sqrt {\pi } \text {erf}(x)+4 c_1\right )}\right )\right \},\left \{y(x)\to \cot ^{-1}\left (\sqrt {e^{x^2} \left (-\sqrt {\pi } \text {erf}(x)+4 c_1\right )}\right )\right \}\right \}\] Maple : cpu = 0.383 (sec), leaf count = 55

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