Early Withdrawal

Question: method of undetermined coefficients?

Find a particular solution to the differential equation

y”+5y’+6y=72t^3

y= ?

Answer: y” + 5y’ + 6y = 72t³

Solve for the complimentary solution, y₍(t).

r² + 5r + 6 = 0
(r + 3)(r + 2) = 0
r = -3, r = -2

y₍(t) = C₁e^(-3t) + C₂e^(-2t)

You have to find the particular solution before the initial conditions can be applied to solve for C₁ and C₂.

Make a guess at the particular solution. Since 72t³ is a polynomial, the particular solution, Yᵨ(t), is also a polynomial.

Yᵨ(t) = At³ + Bt² + Ct + D
Yᵨ’(t) = 3At² + 2Bt + C
Yᵨ”(t) = 6At + 2B

Substituting into the DE

6At + 2B + 5(3At² + 2Bt + C) + 6(At³ + Bt² + Ct + D) = 72t³

6At + 2B + 15At² + 10Bt + 5C + 6At³ + 6Bt² + 6Ct + 6D = 72t³

6At³ + (15A + 6B)t² + (6A + 10B + 6C) + (2B + 5C + 6D) = 72t³

Solve for the coefficients:
6A = 72
—-> A = 12

15A + 6B = 0
—> B = -30

6A + 10B + 6C = 0
—> C = 38

2B + 5C + 6D = 0
—> D = -65/3

So Yᵨ(t) = 12t³ – 30t² + 38t – 65/3

The general solution is the sum of the complimentary and particular solutions.

y(t) = y₍(t) + Yᵨ(t)

y(t) = C₁e^(-3t) + C₂e^(-2t) + 12t³ – 30t² + 38t – 65/3

Question: Trust Account Question Concerning Bank Foreclosures?

My mother has $100k in a CD, she also has 3 other CDs in the same bank (Wachovia) for a total of approx $60k. The CDs are in a trust account bearing my brother’s and my name. Q: Because it is a trust acct under 2 people’s names does the $100k FDIC rule apply here (meaning she’s covered under FDIC for the full $160k)? Or is it considered just 1 name (“trust”) and therefore she should get out the $60k ASAP and put it in another bank. Wachovia seems to be in trouble and I don’t want to see her lose $60k (even tho she’d get a penalty for early withdrawal as these CD’s don’t mature till November 2008). TY for responding.

Answer: It is actually insured by the FDIC for $100k per account. You are completely covered for each account.
Wachovia is the worst bank on screwing people. I would take those to Wells Fargo right away. If you can wait til November it would be great, but I’m not sure I would be willing to trust them.
While each account might be covered, it is still in your best interest to get away from them asap. They will underhandedly try and find a way to take peoples money to cover the cost of their dealings under the table. When they go under, they will be fudging paperwork left and right to cover their exec’s who are stealing money. They will especially hit the highest accounts because they figure those are the people who won’t miss a few hundred dollars missing.

Javaid Kiyani – FREE Property CD (Property Investing Investment)

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