Recent content by gkirkland

Homework Statement Determine the non-homogenous solution of the given differential equation. Homework Equations See 3. The Attempt at a Solution I have solved for the homogenous part, but as you can see in the link I am getting an unsolvable system of equations with the...

Ok, so check my logic on this one: If you can form a matrix P (ie: A is an n x n matrix and has n eigenvalues with n independent eigenvectors) B=P^{-1}AP will form a diagonolized matrix and then e^A=P^{-1}e^BP so you reach a solution fairly easily. If A is an n x n matrix and has n eigenvalues...

Ok, I'll keep working on the proof, but in the mean time I'd like to get some instruction on as to how these exponentials are used. For example, if I'm given a matrix A and asked to find the exponential of A these are the steps I take: 1) Find eigenvalues and then eigenvectors of A 2) Form a...

Won't you end up with differing coefficients even with further expansion? such as \frac{1}{4}S^2T^2 - \frac{1}{2}S^2T^2

So I still don't quite understand how they got what they got. Here's is my attempt: http://i4.photobucket.com/albums/y117/The0wnage/Capture_zps52a2608b.jpg I get 7 terms from e^{a+b} but 9 terms from e^ae^b after I distribute and I don't see a way to cancel them all?

Oh ok! So they show the first two terms and "FOIL" it out for simplicity sake. I've been staring at this thing for 20 minutes and can't believe I didn't realize that. That was a great explanation, thanks! Could you also explain the 1/2!(AB+BA) portion in the last line?

Can someone please explain the below proof in more detail? The part in particular which is confusing me is Thanks in advance!

So I calculated the inverted matrix, but for some reason I'm still not getting the correct solution. Can someone please spot my mistake?

I didn't even think about using Cramer's rule to find the inverse! That was a great idea, got it on the first try. Thanks!

I am working on the following problem: Can someone please show or explain the steps to invert the phi matrix? I've given it a few tries, but I can't reach what the book has for the answer. Please help! Thanks

My DE skills are a bit rusty, and I need some help remembering how to handle a system such as: \dot{x_1}=x_2 \dot{x_2}=-2x_1-3x_2+sint+e^t I have found the homogeneous solution to be (sorry I don't know how to do matrices here): c_1\left\{e^{-t}\right\}+c_2\left\{e^{-2t}\right\}...