To be more precise, I want to solve a system of linear  ODE  with periodic coefficients.

a D@@X(t) + b D@X(t)  + C(t) X(t) + D(t) Y(t) = P0

a D@@Y(t) + b D@Y(t)  + C(t) Y(t) -  D(t) X(t) = 0

ONLY C and D are peridic coef.  a,b  are constant.

The unknowns are X(t) and Y(t).

Thanks

Well, this solution is only valid  for t near zero. However t for me is time and it goes to infinity.

x(t) and y(t) are the displacements  of an oscillating structure and should be bounded !

Is it possible to make it in Fourier series ?

regards,