2.76   ODE No. 76

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

\[ -a \cos (y(x))+b+y'(x)=0 \] Mathematica : cpu = 0.15046 (sec), leaf count = 116

\[\left \{\left \{y(x)\to 2 \tan ^{-1}\left (\frac {a \tanh \left (\frac {1}{2} \left (x \sqrt {(a-b) (a+b)}-c_1 \sqrt {(a-b) (a+b)}\right )\right )}{\sqrt {(a-b) (a+b)}}-\frac {b \tanh \left (\frac {1}{2} \left (x \sqrt {(a-b) (a+b)}-c_1 \sqrt {(a-b) (a+b)}\right )\right )}{\sqrt {(a-b) (a+b)}}\right )\right \}\right \}\]

Maple : cpu = 0.049 (sec), leaf count = 54

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