These are differential equations problems. They are now "redo's", so I have hints from the grader that I don't understand.(adsbygoogle = window.adsbygoogle || []).push({});

First problem:

(x^2 + 1)y'' + 6xy' + 4y = 0

After isolating C_n+2, I have this.

(n+2)(n+1)C_n+2 * X^n = -n(n-1)C_n * X^n - 6nC_n * X^n + 4C_n

C_n+2 = [-n(n-1)C_n - 6nC_n + 4C_n] / (n+2)(n+1)

Since the grader is saying my solution for C_n+2 is equal to

[-(n+4) / (n+2)]C_n, it appears that I am right up until this point.

I have simplified the numerator, and it still doesn't look right.

C_n+2 = C_n[-n(n-1) - 6n + 4] / (n+2)(n+1)

It looks like it should be

C_n+2 = C_n[(-n)^2 - 5n + 4]

C_n+2 = C_n[(n-4)(n-1)] / (n+2)(n+1)

Is there a (n+1) in the numerator that cancels?

Second problem:

y'' + xy' + y = 0

y'' = Sigma_n=2 n(n-1)C_nX^n-2

y' = Sigma_n=1 nC_nX^n-1

y = Sigma_n=0 C_nX^n

Sigma_n=2 n(n-1)C_nX^n-2 + Sigma_n=1 nC_nX^n-1 + Sigma_n=0 C_nX^n = 0

Sigma_n=0 (n+2)(n+1)C_n+2X^n + Sigma_n=0 nC_nX^n + Sigma_n=0C_nX^n = 0

X^n[(n+2)(n+1)C_n+2 + nC_nX^n + C_nX^n = 0

X^n(n+2)(n+1)C_n+2 = -X^n(n)C_nX^n - X^nC_n

C_n+2 = -X^n(n)C_n - X^nC_n

C_n+2 = (-nC_n - C_n) / (n+2)(n+1)

Is this incorrect? The grader says this should be

C_n+2 = -C_n / (n+2)

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# Homework Help: Solve Series and Find General Solution

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