Help with 2 Problems in Differential Equations

[ballajr]

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)

Homework Equations

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.

 

[gabbagabbahey]

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.

 

[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)

 

[Mark44]

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