Finding a Transformation Matrix to yield the basis

[silvermane]

Homework Statement

The solutions to the linear differential equation d^2u/dt^2 = u for a vector space. Find two independent solutions, to give a basis for that solution space.

The Attempt at a Solution

I want to understand this question. I feel that there's something I'm missing. I believe that I need to find the Transformation Matrix, but I need to understand how :(

Any hints or tips are greatly appreciated, but please don't give me just an answer! )

 

[hgfalling]

I don't really think you're looking for a transformation matrix here. You have some vector space, with a vector u. There are a bunch of vectors (an infinite number, in fact!) in the space that solve the equation $u'' = u$. What you want is a way to write down any vector that solves that equation as the sum of two other vectors (that you are going to find).

Now, what vectors solve this equation?

 

[silvermane]

Well now... I feel like a noob :D

e^t and e^-t are a basis... I misread the question -.-