Determine a Dif EQ

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December 9th 2007, 09:33 PM
Auxiliary

Determine a Dif EQ

For each of the following, determine a differential equation (or a system of Dif EQ's), which has the expression of what is below for the general sol'n.

1.) $y=c_1\cos(\sqrt{2}t)+c_2\sin(\sqrt{2}t)$

2.) $y=c_1e^{4t}+c_2te^{4t}$

3.) $\textbf{X}=c_1\left(\begin{array}{r}0\\1 \end{array}\right)e^{-3t}+c_2\left(\begin{array}{r} 1\\0 \end{array}\right)e^{2t}$
December 10th 2007, 05:13 AM
TKHunny

Let's think about characteristic equations:

1) Imaginary Solutions?

2) Real, Repeated Solutions?

3) Real, Unequal solutions?
December 10th 2007, 05:15 AM
kalagota

Quote:

Originally Posted by Auxiliary

For each of the following, determine a differential equation (or a system of Dif EQ's), which has the expression of what is below for the general sol'n.

1.) $y=c_1\cos(\sqrt{2}t)+c_2\sin(\sqrt{2}t)$

$\frac{d^2y}{dt^2} + 2y = 0$

Quote:

Originally Posted by Auxiliary

2.) $y=c_1e^{4t}+c_2te^{4t}$

$\frac{d^2y}{dt^2} - 8\frac{dy}{dt} + 16y = 0$
December 10th 2007, 08:45 AM
Auxiliary

Quote:

Originally Posted by kalagota

$\frac{d^2y}{dt^2} + 2y = 0$

$\frac{d^2y}{dt^2} - 8\frac{dy}{dt} + 16y = 0$

Thanks kalagota! How exactly did you come up with those by the way? Was it a trial and error type of deal?
December 10th 2007, 08:52 AM
topsquark

Quote:

Originally Posted by Auxiliary

Thanks kalagota! How exactly did you come up with those by the way? Was it a trial and error type of deal?

Quote:

Originally Posted by kalagota

$\frac{d^2y}{dt^2} + 2y = 0$

Let's turn this around for a moment:

How would you go about solving
$\frac{d^2y}{dt^2} + 2y = 0$

Therein lies your answer...

-Dan
December 10th 2007, 01:09 PM
TKHunny

Quote:

Originally Posted by Auxiliary

Thanks kalagota! How exactly did you come up with those by the way? Was it a trial and error type of deal?

Come on, Aux. there are nearly eyeball problems. You simply MUST read up on the characteristic equation. You can't be struggling here or you'll never make it.
December 10th 2007, 01:24 PM
Auxiliary

Heh, I do very well on the exams. In fact, I have an A in this course. This is just the harder practice that I choose to do as well. I see now that it was quite trivial, although the systems one will take some work.

Thanks for the help.