I have been trying to solve the equation of motion of a particle in a magnetic field. I was able to reduce the equation of motion to a form similar to Mathieu Differential Equation as:
$$y'' + (a + a\cos(2x))y = 0$$
I have tried to find the solution to the above equation using Mathieu functions. However, i seem to be confused on how to proceed with it. Any suggestions are welcome.
Yes, this is a Mathieu equation with $q = -a/2$.
$$y(x) = c_1 \text{C}(a,-a/2,x) + c_2 \text{S}(a,-a/2,x)$$
where $C$ and $S$ are the Mathieu cosine and sine functions.