Can you help me understand why my answer is wrong (system of differential equations, solved via eigenvectors)?

Ah, I think I figured it out, kind of. It seems the formula the professor gave us was wrong? I have a solution, but not via eigenvectors. Would still appreciate help if anyone can offer it.

I wish I could help, but I can’t begin to conceive of the problems you face. I so admire that you are smart enough to face them. Surely we have somebody who can speak and think in this language to help you. Good luck.

I have no idea if this helps because I don’t understand it at all but and I don’t know if you have shown every step… my mother was a mathematician and a Associate Professor of statistics and she once told me that she always had to remind her students, and herself, that when you are doing higher math problems and you don’t arrive at the right answer that the problems if very often not that you haven’t done the “higher math” parts correctly, but that somewhere along the line you added 2+2 and got 5, if you know what I mean. I guess what she was trying to say is that you can rack your brain checking the complex parts, convinced you’ve done one the complex, hard parts wrong, when it’s quite possible that it could be something very simple, that you are overlooking, something like minor computational error. If that is possible I would check for something like that. I just don’t know.

Anyway, I don’t know if that advice helps, but it’s all I’ve got.

Good luck.

Asked my TA this question today and he was stumped. He’s gonna talk to the prof and report back.

When you have a double root for characteristic polynomial and a single eigenvector your solutions are not what you have here:

[x(t)] = (at + b) * e^(eigenvalue*t) * eigenvector
[y(t)]

The solutions are in form (a v1 + b(t v1 + v2)) e^( c t)

Where v1 is the eigenvector and c is the only eigenvalue and v2 is the solution to (cI – A) v2 = v1.

@BonusQuestion Thank you…yeah, that formula that you say is wrong was given to us by the professor during lecture. I was already pretty convinced from my own analysis that that formula was wrong but it helps to hear it from someone else. I’ll try your method.

Yes, the formula is wrong. He probably mistook it with solutions to linear differential equations. If you have a zero c with multiplicity for characteristic polynomial of a linear DE then solutions corresponding to that zero are e^(ct), te^(ct), etc.

Prof admitted in class today that he gave us a wrong formula and taught us the right method. Thanks for all the help!

I’m just glad that you found out what was wrong with the whole business. It was probably quite maddening! When you believe, when you are almost certain, that you’re doing everything right, and it still, just keeps coming out wrong. :-)

@lillycoyote It is maddening! The funny thing is that it’s becoming a bit of a trend; seems like every time I stoop to Fluther for help with my homework it turns out that somebody made a mistake, and it wasn’t me.