Math Help - Two Problems I Need Help With

1. Two Problems I Need Help With

2) Find the General Solution to:
$(D^3 - D^2 + D - I)[y] = t^5 + 1$

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

2. Typo in #3:

2) Find the General Solution to:
$(D^3 - D^2 + D - I)[y] = t^5 + 1$

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

3. Originally Posted by ballajr
Typo in #3:

2) Find the General Solution to:
$(D^3 - D^2 + D - I)[y] = t^5 + 1$

3) Prove or disprove that there are two constants A and B such that:
$t^2D^2 - tD - 8I = (tD + AI)(tD + BI)$
for the first one now you have to do the other side

$(D^3 - D^2 + D - I)[y] = D^6$

$(D-1)(D^2+1)D^6$

$c_{1}e^t +c_{2}\cos{t} +c_{3}\sin{t} +c_{4} +c_{5}t + c_{6}t^2 +c_{7}t^3 +c_{8}t^4 +c_{9}t^5$