2.354   ODE No. 354

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

\[ y'(x) (x \sin (y(x))-1)+\cos (y(x))=0 \] Mathematica : cpu = 0.0658719 (sec), leaf count = 145

\[\left \{\left \{y(x)\to -\cos ^{-1}\left (\frac {c_1 x-\sqrt {c_1^2-x^2+1}}{c_1^2+1}\right )\right \},\left \{y(x)\to \cos ^{-1}\left (\frac {c_1 x-\sqrt {c_1^2-x^2+1}}{c_1^2+1}\right )\right \},\left \{y(x)\to -\cos ^{-1}\left (\frac {\sqrt {c_1^2-x^2+1}+c_1 x}{c_1^2+1}\right )\right \},\left \{y(x)\to \cos ^{-1}\left (\frac {\sqrt {c_1^2-x^2+1}+c_1 x}{c_1^2+1}\right )\right \}\right \}\]

Maple : cpu = 0.047 (sec), leaf count = 115

\[ \left \{ y \left ( x \right ) =\arctan \left ( {\frac {{\it \_C1}}{{{\it \_C1}}^{2}+1} \left ( -{\it \_C1}\,x+\sqrt {{{\it \_C1}}^{2}-{x}^{2}+1} \right ) }+x,-{\frac {1}{{{\it \_C1}}^{2}+1} \left ( -{\it \_C1}\,x+\sqrt {{{\it \_C1}}^{2}-{x}^{2}+1} \right ) } \right ) ,y \left ( x \right ) =\arctan \left ( -{\frac {{\it \_C1}}{{{\it \_C1}}^{2}+1} \left ( {\it \_C1}\,x+\sqrt {{{\it \_C1}}^{2}-{x}^{2}+1} \right ) }+x,{\frac {1}{{{\it \_C1}}^{2}+1} \left ( {\it \_C1}\,x+\sqrt {{{\it \_C1}}^{2}-{x}^{2}+1} \right ) } \right ) \right \} \]