- #1
lordsurya08
- 4
- 0
Homework Statement
Find two power series solutions of the DE
(x+2)y'' + xy' - y = 0
about the ordinary point x = 0 . Include at least first four nonzero terms for each of the solutions.
2. The attempt at a solution
I distributed the y'' term and substituted
y = Ʃ0inf cnxn
and its derivatives into the DE. I equated it to 0 and got two equations:
2c2 - c0 = 0
xn(cn+1*n(n+1) + cn+2*(n+1)(n+2)+ cn*(n-1)) = 0
The weird thing is that the second equation (the recurrence relationship) has three c terms in it, although the examples shown have two. How do I get c2 and c0? After that happens should I simply solve for c1 using the recurrence relationship with n = 0?