Homework Questions/MA266Fall10

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I was doing supplemental problem A and found:

$ e^{-2t}(2A-2At^2+4At-3)=0. $

So if t=0 then A=3/2 And: $ e^{-2t}(-4Bt+4B-3)=0. $

So if t=0 then B=4/3

But with the variable t I wasn't sure if these answers were enough for A and B or if I needed to find more possibilities, which I had no clue how to do.

ANSWER: You need to find values of A and B that work for all t (if there are any). Also, I think you made a mistake when taking the derivatives. Note that the derivative of $ e^{-2t} $ is $ -2 e^{-2t} $.

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Basic linear algebra uncovers and clarifies very important geometry and algebra.

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