Help with 2 problems!

1. Mar 22, 2010

ballajr

1. The problem statement, all variables and given/known data

1) Find the General Solution to:
(D3 - D2 + D - I)[y] = t5 + 1

2) Prove or disprove that there are two constants A and B such that:
t2D - tD - 8I = (tD + AI)(tD + BI)

2. Relevant equations

3. The attempt at a solution

1) I can't figure out how to attempt this one. Doesn't make sense to me.
2) I should FOIL out the RHS of the equation, but I did that on paper and it didn't make too much sense to me.

2. Mar 22, 2010

gabbagabbahey

There are two methods that immediately come to mind:

(1)Use the method of Undetermined Coefficients

(2)Use the annihilator method

Show us what you've got, and keep in mind that to calculate something like $D(tD)$ you need to use the product rule.

3. Mar 23, 2010

ballajr

There was a typo in #2:

2) Prove or disprove that there are two constants A and B such that:
t2D2 - tD - 8I = (tD + AI)(tD + BI)

4. Mar 24, 2010

Staff: Mentor

There are solutions for A and B if you permit complex solutions.