I have a non-linear differential equation of the form-
$$ A \ddot{x} + B \dot{x}^2 + C x = \dot{u} + u^2 $$
In the above $u$ is the external input and the output signal is $x$. I can solve the system numerically by putting in a sigal in place of $u$ say $u(t)=u_0\sin{\omega t}$ or any other function. But what if I want to put in a generalised function in place of $u$ say $u(t) = \frac{b_0}{2} + \sum{a_n}\sin{\omega_n t} + \sum{b_n}\cos{\omega_n t}$ using Fourier's series? Please provide me a generalised framework for the process.