Rewrite the following differential equation as an equivalent system of first-order differential equations. Use the variables
x1=x x2=x' x3=x'', etc.
(so that your equations will have the form x2'=x3, etc.: denote subscripts by appending the subscript to the variable name: X1= x1)

Equation to rewrite:
x''''+20x''−13x'+17x=−5cos(9t)

x1' =
x2' =
x3' =
x4' =

Question

Rewrite the following differential equation as an equivalent system of first-order differential equations. Use the variables
x1=x    x2=x'    x3=x'', etc.
(so that your equations will have the form x2'=x3, etc.: denote subscripts by appending the subscript to the variable name: X1= x1)

Equation to rewrite:
x''''+20x''−13x'+17x=−5cos(9t)

x1' =
x2' =
x3' =
x4' =

eyust707 · Answer

$x _{1} = x$
$x _{2} = x'$
$x _{3} = x''$
$x _{4} = x'''$
$x _{5} = x''''$

anonymous · Answer

how do solve for those values though

eyust707 · Answer

Im not exactly sure...

I know they are saying that
$$x _{2}'=x'' = x _{3}$$

anonymous · Answer

yea i got that too but im not sure what else were supposed to be doing ijn order to get those values

eyust707 · Answer

im gunna go read a little and try and figure this out. maybe by that time someone like @TuringTest or @dpaInc  can help you

anonymous · Answer

ok thank you and I will continue reading as well

eyust707 · Answer

what is the section of your diffs book that this cam from titled?

eyust707 · Answer

http://www.phaser.com/modules/elaydi/content/helptips/secondorderode.html

anonymous · Answer

it wasn't from my book it was from an online web homework site and ive been looking in the book for similar problems and can't find it

anonymous · Answer

but i assume it has something to do with first-order systems

eyust707 · Answer

is this the first one in the homework?

anonymous · Answer

yes

eyust707 · Answer

Simply rearranging we can say this: 
$x''''=-20x''+13x'-17x−5\cos(9t)$
Then using what we said earlier:
$x_{4}' = -20x''+13x'-17x−5\cos(9t)$

eyust707 · Answer

But now we are second order

anonymous · Answer

i do not think thats what its asking. I do believe it is first order systems

eyust707 · Answer

so:

$$x_{4}' = -20x_{2}'+13x'-17x−5\cos(9t)$$

eyust707 · Answer

and your system also includes these equations:

anonymous · Answer

yes but i think what we're supposed to it is know that x''''=f(t,x,x',x'',x''') and then we use what they gave us to solve for the answers. we know that x1=x and x2=x'=x1' and x3=x''=x2' and x4=x''''=x1'''=x2''=x3'

anonymous · Answer

so we get
x1'=x2
x2'=x3
x3'=x4
x4'=?

eyust707 · Answer

$x_{1}' = x_{2}$
$x_{2}' = x_{3}$
$x_{3}' = x_{4}$
$x_{4}' =-20x_{2}'+13x'-17x−5\cos(9t) $

anonymous · Answer

do we need to substitute anything in

eyust707 · Answer

honestly im not exactly sure what form they want the variables of the last equation

eyust707 · Answer

We are definatley close tho... lol

anonymous · Answer

lol yes we are thank you

eyust707 · Answer

In this one they put them in terms of $x_{1}$ and $x_{2}$ http://www.phaser.com/modules/elaydi/content/helptips/secondorderode.html

eyust707 · Answer

plus all the other equations are in those terms... so might as well.

anonymous · Answer

ok let me try it and see what happens

anonymous · Answer

woo it works!! I guess it wasnt as complicated as it seemed to be! we didhave to replace the variables

eyust707 · Answer

=P

eyust707 · Answer

yes diffs is weird stuff... just flat out weird..

anonymous · Answer

yea i agree! lol

eyust707 · Answer

whats even weirder is that theres all sorts of natural phenomenon that somehow fit themselves into the solution to differential equations...

anonymous · Answer

i know!

anonymous · Answer

differential equations is a very interesting subject