Question

How do I use the exponential shift to solve the linear differential equation y'' + 7y' +12y = 2(e^-3)(cos2x)

Answer 1

im looking to find the general solution y = yc +yp. so far i have solved the homogenous part of the equation yc. yc = Ae^-3x + Be^-4x. i cant solve for yp yet.

Answer 2

ok

Answer 3

Let me do it on paper first. I think it would be murder typing it out.

Answer 4

haha thank you! any help will go a long way

Answer 5

i'll continue to try draw something out of my mess of numbers and letters while i wait

Answer 6

i also figured that the derivative operator 'D' helps so that the LHS = (D^2 + 7D +12)y

Answer 7

You do mean e^{-3x}, don't you?

Answer 8

yes! sorry typo

Answer 9

When I get to factors that need expanding, I'm going to get Mathematica to do that (save time).

Answer 10

ok no worries. if i dont follow il just let u know

Answer 11

So what happened, your lecturer just dump theory on you with no demonstration?

Answer 12

he demonstated with the d.e. y'' + 6y' + 13y = x(e^3x)(sin2x) however that takes y = imaginary(Y) and also takes into account the complex numbers. As my roots are reall -3, -4 and i take y=real(Y) instead, i dont know what yp to try

Answer 13

he pretty much chalk vomits all over the board without going into the specifics of how he gets to places

Answer 14

Not trained to teach...

Answer 15

its really quite frustrating... luckily we are changing lecturers next week.. sorry for any hassle im causing you!

Answer 16

just give me a fan point and i'll be happy

Answer 17

wow thanks! im just gona go through it and check i understand.. haha ok sure how do i do that?

Answer 18

just click my 'become a fan' link...if there isn't one there, refresh the page...should work then

Answer 19

ps. is there a place to download mathmatica for free? ok right on it

Answer 20

www.wolframalpha.com

The guy who made mathematica made this site. It can do a lot of things like integration, solving differential equations, plotting, etc.

Answer 21

fanned. thanks a million! will i still be able to ask help from you if i have any more troubles..

Answer 22

this is wolfram's solution to your equation

http://www.wolframalpha.com/input/?i=y%27%27-2y%27%2B5y+%3D+16x^3*e^%283x%29+++

Answer 23

woops...no it's not...wait.

Answer 24

haha! i was like crap.. i did notttttt get that

Answer 25

http://www.wolframalpha.com/input/?i=y%27%27%2B7y%27%2B12y+%3D+2e^%28-3%29cos%282x%29

Answer 26

haha ur awesome at pen to paper but im afraid you did the same typo as me last time. theres an 'x' in e^-3x. however the graphs dont look how i thought they would..

Answer 27

graphs in the correct version*

Answer 28

ah...typo...

Answer 29

yep :) i thought it would have more of a decaying oscillation as it is overdamped.. is it because of the negative exponential? why?

Answer 30

So, am I right in understanding you've finished deriving the solution?

Answer 31

And you're reading off that and not Wolfram?

Answer 32

sorry no. i was comparing my notes to the graphs of wolfram.. but! i havent read through the wolfram content yet.. just making observations. if you would like you can continue helping other students.. and im guessing when i need help again it will notify you?

Answer 33

Yes, I get an e-mail if you respond to a thread I've been in.

Are you fine to derive the rest?

Answer 34

If an error's been made on my part, it's because it's after 1am where I am.
If you need help in the next ~12-24hrs, I may not be around. You'd should try your luck with someone else.

Answer 35

i should be ok for now thanks :) it takes me quite a while longer than you to come up with a solution

Answer 36

yep me too. 1:22am. ok do u recommend anyone else?

Answer 37

I don't know the particular skill level of people on here. You may have to post and cross fingers.

Answer 38

Is this an assignment due tomorrow or something?

Answer 39

ahah yeh you caught me out. due 2pm. i wish i could say im a more dedicated student working til the early hours of the morning doing maths... ah the thrills of life!

Answer 40

Well, since your timezone's mine, if I see something from you in the morning and I can respond, I will. My day will be hell busy, though.

Answer 41

Anyways, good luck. I seriously have to hit the sack.

Answer 42

thanks you are a hero! night!