Question

(D4 - 5D3 + 5D2 + 5D - 6)y = 0 Find the General Solution ( I doubt any of you can haha)

Answer 1

`My interpretation:` \(D\) is the linear differential operator.
Since no independent variable is given, will call it \(t\).

(I'm not going to go through the algebra right now;
you should know this part by now ... Yes, it's long!)

\(\color{black}{\displaystyle (D^4 - 5D^3 + 5D^2 + 5D - 6)[y] = 0}\)
\(\color{black}{\displaystyle (D-1)(D+1)(D+2)(D+3)[y] = 0}\)

Next, just a primitive step to write out the general solution.
(No repeated roots, no imaginary roots, ... should be pretty easy.)