I desperately need to solve a coupled system of linear second order differential equations of the form:
$ a_1x''+ b_1x' + c_1y'' + d_1y' =0 $
$ a_2x'' + b_2x' + c_2y'' + d_2y' + e_2y = 0 $
initial conditions are :
$ y(0)=y_0, y'(0)=x(0)=x'(0)=0. $
x and y are displacement in time.
What method do you suggest for solving this system? Any suggestion will be appreciated!