Differential Equations Homework- Find General Solution

[ballajr]

Homework Statement

1) Find the general solution to:
(t²D² - 2tD - 28I)[y] = (-17 + 48t - 97t² + 6t³)e^-t

2) Find the general solution to:
(D + tI)²[y] = 3 + 3t + 6t² + t³+ t⁴

Homework Equations

The Attempt at a Solution

1. I think for this one, I just need to distribute the exponential and then use the annhilator method to do some work. I am a bit confused about this differential operators chapter.

2. This one, I just tried to foil out the RHS to find a way to make it equal to the other side, but it didn't work

 

[mighty2000]

out. I'm not sure what to do next.

For the first problem, you are on the right track. Distributing the exponential and using the annhilator method are important steps in finding the general solution. As for your confusion with the differential operators chapter, I suggest reviewing the material and practicing some examples to gain a better understanding.

For the second problem, foiling out the RHS may not be the most efficient approach. Instead, try using the power series method to solve for the general solution. This method involves representing the solution as a series of powers of t and solving for the coefficients. I hope this helps. Good luck with your homework!