- #1
kahless2005
- 46
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Given:
y'+2xy=0
Find:
Write sereis as an elementary function
My solution so far:
y=[Sum n=0, to infinity]C(sub-n)*x^n
y'=[Sum n=1, to infinity]n*C(sub-n)*x^(n-1)
y' can be transformed into:
=[Sum n=0, to infinity](n+1)*C(sub-n+1)*x^n
([Sum n=0, to infinity](n+1)*C(sub-n+1)*x^n) + 2x([Sum n=0, to infinity]C(sub-n)*x^n)=0
([Sum n=0, to infinity](n+1)*C(sub-n+1)*x^n) +2([Sum n=0, to infinity]C(sub-n)*x^(n+1))=0
My question:
Can I transform [Sum n=0, to infinity]C(sub-n)*x^(n+1) into ([Sum n=1, to infinity]C(sub-n-1)*x^(n)?
If so, then y(x)=([Sum n=,0. to infinity]((-1)^(n+1)*C(sub-o)*x^(n+1)*2^(n-1))/n!
How do I transform that into an elementary function?
Sorry about the ugly typing...
y'+2xy=0
Find:
Write sereis as an elementary function
My solution so far:
y=[Sum n=0, to infinity]C(sub-n)*x^n
y'=[Sum n=1, to infinity]n*C(sub-n)*x^(n-1)
y' can be transformed into:
=[Sum n=0, to infinity](n+1)*C(sub-n+1)*x^n
([Sum n=0, to infinity](n+1)*C(sub-n+1)*x^n) + 2x([Sum n=0, to infinity]C(sub-n)*x^n)=0
([Sum n=0, to infinity](n+1)*C(sub-n+1)*x^n) +2([Sum n=0, to infinity]C(sub-n)*x^(n+1))=0
My question:
Can I transform [Sum n=0, to infinity]C(sub-n)*x^(n+1) into ([Sum n=1, to infinity]C(sub-n-1)*x^(n)?
If so, then y(x)=([Sum n=,0. to infinity]((-1)^(n+1)*C(sub-o)*x^(n+1)*2^(n-1))/n!
How do I transform that into an elementary function?
Sorry about the ugly typing...