Begin with the series solution y-? ~anz" to derive the recursive relation (n +2)(n +1)an+ -an-2, n2 2 for the differential equation y+2y0 and write out the first six non-zero terms.

I guess the ODE is supposed to be

So if

then

so that

for , or equivalently,

for . Note the dependency between every other coefficient - this means we can consider two cases:

and so on, with

and so on, with

Then the ODE has solution

and the first six non-zero terms occur for , for which we get

21

step-by-step explanation: