4.22   ODE No. 1022

\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) + \left ( a\cos \left ( 2\,x \right ) +b \right ) y \left ( x \right ) =0} \]

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

Mathematica: cpu = 0.027003 (sec), leaf count = 28 \[ \left \{\left \{y(x)\to c_1 \text {MathieuC}\left [b,-\frac {a}{2},x\right ]+c_2 \text {MathieuS}\left [b,-\frac {a}{2},x\right ]\right \}\right \} \]

Maple: cpu = 0.156 (sec), leaf count = 21 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{\it MathieuC} \left ( b,-{ \frac {a}{2}},x \right ) +{\it \_C2}\,{\it MathieuS} \left ( b,-{\frac { a}{2}},x \right ) \right \} \]