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So I had an exam and got this problem wrong, that I had done incorrectly on the quiz as well. comments in red under picture are comments from professor.

here is the work:

Attempt)

Why is this general solution? What is the fundamental set? What is y

So on the exam, in addition to what I did, I should of found the first, second, and third derivatives of each y

And uh, WOW. I could of sworn I wrote out y

here is the work:

Attempt)

Why is this general solution? What is the fundamental set? What is y

_{p}? (this should be verified)So on the exam, in addition to what I did, I should of found the first, second, and third derivatives of each y

_{1,2,3}and then separately substitute them into the non homogeneous eqn to check for validity?And uh, WOW. I could of sworn I wrote out y

_{p}.. So if write y_{p}=2x-12x^{2}e^{x}that would satisfy that part right?
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