The solution is strongly related to the integral...
... that can be solved integrating 'term by term' the expansion...
I am trying to solve what I thought was going to be a simple differential equation.
So I set
Then separating variables and integrating I got
Solving for y
remembering we can again separate variables
This is where I get stuck. I know this should be integrable to a sinusoid, but I don't know how. The actual question asks you to prove that the solution oscillates with a period proportional to where A is the amplitude.
Any help would be appreciated.