If you show us what you tried, it will give us a much better idea where your problems (if any) lie.
I am trying to do this problem and I am not sure about the method I need to use.
So far I have used the ansatz and found the first and second derviatives and put them into the ODE and collected the powers of E.
Then I used the intital conditions on the ansatz
Am I doing this right and where would that trig identity come into this problem?