Quote:
Originally Posted by Joshua2
so I have two part question.
I have a 2nd order linear homogeneous equation but the initial values aren't at y(0) and y'(0) like normal. They are @ 2 instead. So it seems there may be three ways to go about it. The first I thought of was to pretend it is at 0 and then try to shift the answer,

You need to go back and learn some linear algebra. In particular,
look up "affine linear transform".
Quote:
but that is hard for complicated equations. I could also just plug everything in and solve two equations with two unknowns, but it is a lot of algebra. I think the teacher had a third way that might be the easiest similar to my 2nd way, but I couldn't understand it.
2nd question is solving inhomogeneous 2nd order linear
so our teacher has us solving these with an alpha beta method I don't really understand. But its solving to easier equations. let u=y'+ay and u' + Bu = the left hand side of the equation y'' + cy' + d. I couldn't find anyone on the net who used this method and explained. Everyone seems to use complicated stuff like Lagrange or Fourier or Wronskian

One difficulty you are having is simply sloppy thinking in general.
You seem unable to express what you really mean. The
comments above are "word salad". They are very poorly expressed.
The fact that you characterize various methods as "complicated stuff" really
shows that you lack fundamental understanding of what you are doing. I
don't know you personally, but from the comments you have made, it seems
that you shouldn't be taking this class. You have insufficient background.
Further, you seem to be learning the material as "pseudomathematics".
(according to Andre Toom). You are trying to learn the material as
"plug and chug" mechanical manipulations without any UNDERSTANDING
of what is going on.
If you came to me as a student, asking for office hours help, I would give
the following advice:
Quit this class. Go back and take a class in linear algebra. You don't
seem to understand e.g. what the Wronskian is, where it arises, what it
is used FOR, and why it can be used in solving DiffEq's.
I am not sure that I understand your use of Fourier's name.
Certainly you can't be using Fourier Transforms?? Their use is way
beyond your level of understanding.
There are also several different things that can be ascribed to Lagrange
in this context.
You need to be able to express yourself PRECISELY if you are to
have any hope of understanding this material. Stop the handwaving.