Question

Question:
use the fact that y=e^3x is an obvious of each of the following equation to find a second and the general solution.

a: y''-6y''+9=0
b: xy''-3(x+1)y'+9y=0

Answer 1

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Answer 2

y''-6y'+9=0
auxiliary eq. : \[\lambda ^{2} -6\lambda +9=0\]
has one root: 3
so the general solution in this case is (A+Bx)e

Answer 3

\[(A+Bx)e ^{3x}\]

Answer 4

for the B part ask someone else, I am not sure

Answer 5

for b:

e^3x . e^ln-3

im not sure and i need help about b