I am given this ODE:
$$\sin(y''+\epsilon y)+y=1+ \sin\epsilon +\epsilon \sin t$$
And it is given that:
$$y(0)= \cos \epsilon$$ $$y'(0)=\sin \epsilon$$
where $\epsilon \approx 0$ and $t\in[-\delta, \delta]$
It is clear this ODE should be linearized, but with the additional parameter and the inexplicit $y''$, I'm having trouble understanding how to tackle the problem correctly.
Any help would be greatly appreciated!