# Linear systems of differential equations

• Apr 27th 2007, 07:08 PM
SoBeautiful
Linear systems of differential equations
Find the general systems of differential equations. You must use the method that includes matrices, eigen values, and eigen vectors. Carefully identify all the important steps.

y1 = y1 + 4y2 - 2cos t

y2 = y1 + y2 - cos t + sin t

I'm sorry, but I can't figure out how to make this stuff work! I rermember how to do most of the steps, I think, but it isn't working together. This is a practice problem, but my teacher assured me that there will be one just like it on the test on Monday, April 30. Could someone please show me how to do this so that I will know how to work on like it on the test?!?!? Thank you.
• Apr 28th 2007, 06:08 AM
topsquark
Quote:

Originally Posted by SoBeautiful
Find the general systems of differential equations. You must use the method that includes matrices, eigen values, and eigen vectors. Carefully identify all the important steps.

y1 = y1 + 4y2 - 2cos t

y2 = y1 + y2 - cos t + sin t

I'm sorry, but I can't figure out how to make this stuff work! I rermember how to do most of the steps, I think, but it isn't working together. This is a practice problem, but my teacher assured me that there will be one just like it on the test on Monday, April 30. Could someone please show me how to do this so that I will know how to work on like it on the test?!?!? Thank you.

Is there a mistake? Your equations simplify to:
y2 = (1/2)cos(t)
and
y1 = cos(t) - sin(t)
which are independent and don't need any special methods to solve. (Not to mention, they aren't even differential equations!)

-Dan
• Apr 28th 2007, 07:33 AM
CaptainBlack
Quote:

Originally Posted by SoBeautiful
Find the general systems of differential equations. You must use the method that includes matrices, eigen values, and eigen vectors. Carefully identify all the important steps.

y1 = y1 + 4y2 - 2cos t

y2 = y1 + y2 - cos t + sin t

I'm sorry, but I can't figure out how to make this stuff work! I rermember how to do most of the steps, I think, but it isn't working together. This is a practice problem, but my teacher assured me that there will be one just like it on the test on Monday, April 30. Could someone please show me how to do this so that I will know how to work on like it on the test?!?!? Thank you.

Do you mean:

d/dt(y1) = y1 + 4y2 - 2cos t

d/dt(y2) = y1 + y2 - cos t + sin t

RonL
• Apr 28th 2007, 08:04 AM
SoBeautiful
clarification
The problem looks like y(1, 1) just like Integrals are set up. It looks like y from 1 to 1 and the second one looks like y from 2 to 1. I think maybe that is just a way to make it look different than the y's on the other side of the equation???
• Apr 28th 2007, 08:10 AM
CaptainBlack
Quote:

Originally Posted by SoBeautiful
The problem looks like y(1, 1) just like Integrals are set up. It looks like y from 1 to 1 and the second one looks like y from 2 to 1. I think maybe that is just a way to make it look different than the y's on the other side of the equation???

No the left hand sides are y_1 prime and y_2 prime, they are the derivatives
of y_1 and y_2.

RonL
• Apr 28th 2007, 08:14 AM
Hollysti
Oh, ok that makes more sense. Do you think you could help me with the first few steps so that I know how to get started? Or maybe an outline of what exactly I am supposed to do for the problem?
• Apr 28th 2007, 08:25 AM
Hollysti
I have a problem that looks a lot like this one for my next assignment
• Apr 29th 2007, 11:45 AM
SoBeautiful
Thanks for the clarification on y1 and y2 prime, but I still am not sure that I will be able to work a problem like this on the test tomorrow, so if anyone could help me out with this one, I would REALLY appreciate it. Thanks.