\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) + \left ( a \left ( \cos \left ( x \right ) \right ) ^{2}+b \right ) y \left ( x \right ) =0} \]
Mathematica: cpu = 0.014502 (sec), leaf count = 44 \[ \left \{\left \{y(x)\to c_1 \text {MathieuC}\left [\frac {1}{2} (a+2 b),-\frac {a}{4},x\right ]+c_2 \text {MathieuS}\left [\frac {1}{2} (a+2 b),-\frac {a}{4},x\right ]\right \}\right \} \]
Maple: cpu = 0.141 (sec), leaf count = 29 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{\it MathieuC} \left ( {\frac {a}{2}}+b,-{\frac {a}{4}},x \right ) +{\it \_C2}\,{\it MathieuS} \left ( {\frac {a}{2}}+b,-{\frac {a}{4}},x \right ) \right \} \]