\[ y(x) \left (a \cos ^2(x)+b\right )+y''(x)=0 \] ✓ Mathematica : cpu = 0.0095474 (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 = 0.19 (sec), leaf count = 29
dsolve(diff(diff(y(x),x),x)+(a*cos(x)^2+b)*y(x)=0,y(x))
\[y \left (x \right ) = c_{1} \MathieuC \left (\frac {a}{2}+b , -\frac {a}{4}, x\right )+c_{2} \MathieuS \left (\frac {a}{2}+b , -\frac {a}{4}, x\right )\]