\[ y(x) \left (a \cos ^2(x)+b\right )+y''(x)=0 \] ✓ Mathematica : cpu = 0.0269298 (sec), leaf count = 44
DSolve[(b + a*Cos[x]^2)*y[x] + Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to c_1 \text {MathieuC}\left [\frac {1}{2} (a+2 b),-\frac {a}{4},x\right ]+c_2 \text {MathieuS}\left [\frac {1}{2} (a+2 b),-\frac {a}{4},x\right ]\right \}\right \}\] ✓ Maple : cpu = 0.211 (sec), leaf count = 39
dsolve(diff(diff(y(x),x),x)+(a*cosh(x)^2+b)*y(x)=0,y(x))
\[y \left (x \right ) = c_{1} \MathieuC \left (-\frac {a}{2}-b , \frac {a}{4}, i x \right )+c_{2} \MathieuS \left (-\frac {a}{2}-b , \frac {a}{4}, i x \right )\]