2.1022   ODE No. 1022

\[ y(x) (a \cos (2 x)+b)+y''(x)=0 \]

✓ Mathematica : cpu = 0.0088949 (sec), leaf count = 28

DSolve[(b + a*Cos[2*x])*y[x] + Derivative[2][y][x] == 0,y[x],x]
 

\[\left \{\left \{y(x)\to c_1 \text {MathieuC}\left [b,-\frac {a}{2},x\right ]+c_2 \text {MathieuS}\left [b,-\frac {a}{2},x\right ]\right \}\right \}\]

✓ Maple : cpu = 0.332 (sec), leaf count = 21

dsolve(diff(diff(y(x),x),x)+(a*cos(2*x)+b)*y(x)=0,y(x))
 

\[y \left (x \right ) = c_{1} \operatorname {MathieuC}\left (b , -\frac {a}{2}, x\right )+c_{2} \operatorname {MathieuS}\left (b , -\frac {a}{2}, x\right )\]