Find at least the first four nonzero terms in a power series expansion about x=0 for a general solution.
y'+(x+2)y=0

Question

Find at least the first four nonzero terms in a power series expansion about x=0 for a general solution.
y'+(x+2)y=0

amistre64 · Answer

how far have you gotten?

anonymous · Answer

I listed the series and the derivatives but after I distribute the (x+2) I get the wrong numbers. I think I may be distributing wrong? But I am not sure.

anonymous · Answer

(a1+2a2x+3a3x^2+4a4x^3)+(a0x+a1x^2+a2x^3+a3x^4)+(2a0+2a1x+2a2x^2a3x^3)=0

adamaero · Answer

This probably won't help, but you may be able to look at some examples from my book: https://worldtracker.org/media/library/Mathematics/Calculus/Stewart%20-%20Calculus%20-%20Early%20Transcendentals%206e%20HQ%20(Thomson,%202008).pdf#page=765

amistre64 · Answer

a power series (and their derivatives) is of the form
$$y=\sum_0a_nx^n$$
$$y'=\sum_1a_n~nx^{n-1}$$
$$y''=\sum_1a_n~n(n-1)x^{n-2}$$
etc ..