Question

help solve the D.E.

Answer 1

What's "D.E.?"

Answer 2

\((x^2+1)y''+xy-y=0\)

about x=0

Answer 3

differentual equation

Answer 4

so far I have \[(x^2+1)\sum_{n=2}^{\infty}n(n-1)c_nx^{n-2}+x \sum_{n=1}^{\infty}nc_nx^{n-1}-\sum_{n=0}^{\infty}c_nx^n\]

Answer 5

then i plug in to get \[\sum_{n=2}^{\infty}n(n-1)c_nx^{n}+\sum_{n=2}^{\infty}n(n-1)c_nx^{n-2}+\sum_{n=1}^{\infty}nc_nx^n-\sum_{n=0}^{\infty}c_nx^n\]

Answer 6

i change power series 1 to zero? and also power series 3 to zero. and also bring down power series 2 by shifting the index to get:

\[\sum_{n=0}^{\infty}n(n-1)c_nx^n+\sum_{n=0}^{\infty}(n+1)(n+2)c_{n+2}x^n+\sum_{n=0}^{\infty}nc_nx^n-\sum_{n=0}^{\infty}c_nx^n\]
right? do i still take out terms??