# Help with 2 problems!

## Homework Statement

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)

## 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.

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gabbagabbahey
Homework Helper
Gold Member
1) I can't figure out how to attempt this one. Doesn't make sense to me.
There are two methods that immediately come to mind:

(1)Use the method of Undetermined Coefficients

(2)Use the annihilator method

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

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)

Mark44
Mentor
There are solutions for A and B if you permit complex solutions.