Solving 2nd order ODE How would you this ODE: 
$$x''+x+\cos^3t=0$$
The homogenous solution is $x=C\cos t$ so $C\cos t$ is term is part of the solution. But how would you go from there?

The solution of the ode
$$ x''+x=0 $$
should be
$$ x(t) = c_1\cos(t)+c_2\sin(t). $$
Added: For the particular solution you can use variation of parameters method.
