Need quick help with Series, it will only take a few seconds

[twisted079]

So the differential equation I have to solve using power series is
y''-xy=0 when x0 = -1

So i set it up
Ʃ(n+2)(n+1)a_n+2(x+1)ⁿ - x Ʃ a_n(x+1)ⁿ

I know how to generally solve equations like this, but I never solved one like this, where I have to distribute the x ... x(x+1)ⁿ ... I just need to figure this part out (I know I left out the n=0 to ∞)

 

[twisted079]

Ok I figured it out using a cheap (but valid) math trick... in case anyone is wondering...

xƩa_n(x+1)ⁿ = (x+1-1)Ʃa_n(x+1)ⁿ

Now the x+1 can be distributed to give -Ʃa_n(x+1)ⁿ⁺¹

...anyone care to double check me on this?

 

[Mute]

Ok I figured it out using a cheap (but valid) math trick... in case anyone is wondering...

xƩa_n(x+1)ⁿ = (x+1-1)Ʃa_n(x+1)ⁿ

Now the x+1 can be distributed to give -Ʃa_n(x+1)ⁿ⁺¹

...anyone care to double check me on this?

Yep, that's the trick you want to use.