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 = 0.556262 (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 = 0.434 (sec), leaf count = 55

\[\left \{y \left (x \right ) = -\arcsin \left (\frac {1}{\sqrt {-2 c_{1} {\mathrm e}^{x^{2}}-\sqrt {\pi }\, \erf \left (x \right ) {\mathrm e}^{x^{2}}+1}}\right ), y \left (x \right ) = \arcsin \left (\frac {1}{\sqrt {-2 c_{1} {\mathrm e}^{x^{2}}-\sqrt {\pi }\, \erf \left (x \right ) {\mathrm e}^{x^{2}}+1}}\right )\right \}\]