Problem
Find the
Using expanded notation for series I can get an answer that matches up with maple:
What I can't seem to do is find this with a closed form notation for series.
My attempt
First I substitute...
Then I try to get everything to be to power of n...
Then I try to get everything to the same index by taking out n=0 elements where necessary...
Using initial conditions:
The recurrence relationship I get is:
But this is wrong because if I plug in n=2, I get
Where did I go wrong?
Because semplicity is always the best alternative, the initial values problem is
(1)
If we suppose that x(t) is analytic in x=0 it will be...
(2)
The initial conditions give us...
The (1) permits us to derive...
(2)
Deriving (1) we obtain...
(3)
Deriving (3) we obtain...
(4)
Deriving (4) we obtain...
(5)
In general is...
(6)
Kind regards