# Thread: Find the General Solutions

1. ## Find the General Solutions

1) Find the general solution to:
$\displaystyle (t^2D^2 - 2tD - 28I)[y] = (-17 + 48t - 97t^2 + 6t^3)e^{-t}$

2) Find the general solution to:
$\displaystyle (D + tI)^2[y] = 3 + 3t + 6t^2 + t^3 + t^4$

2. Originally Posted by ballajr
1) Find the general solution to:
$\displaystyle (t^2D^2 - 2tD - 28I)[y] = (-17 + 48t - 97t^2 + 6t^3)e^{-t}$

2) Find the general solution to:
$\displaystyle (D + tI)^2[y] = 3 + 3t + 6t^2 + t^3 + t^4$
Dear ballajr,

What is "I" in these two problems?? Is it another variable or a constant value??

3. The I corresponds to a 1. So it can be ignored. The D is the differential operator.

4. Originally Posted by ballajr
The I corresponds to a 1. So it can be ignored. The D is the differential operator.
Dear ballajr,

Sorry for the late answer. Don't have much spare time because of exams. Anyway the first problem could be done by using the substitution, $\displaystyle t=e^u$ and in the second problem you have to find the particular solution and the complimentary function seperately. Try to do these problems using these tips. If you have any questions please don't hesitate to reply back.

Hope this helps.