I'm having issues understanding/solving this question I got for an exam:
Consider this nonlinear differential equation (1): $x''(t) + \cos(x(t))\cdot x(t) = \sin(t)$
Suppose $x$ is small and make an expansion of $\epsilon\cdot x$ in (1) of the form $\epsilon\cdot x = x_0\cdot \epsilon + x_1\cdot \epsilon^2 + x_2\cdot \epsilon^3 + ...$
Question: Find the equations for
- the lowest order of $\epsilon$
- the second lowest order of $\epsilon$
The equations are NOT supposed to be solved. Any help would be greatly appreciated!