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I am stuck when im at this stage:
\[Y(s)(s+6)+3X(s)=\frac{ 8-s(s-1) }{ s-1 }\]

you've got 2 different variables in there? y and x
so y = x', yes?

how does y=x'?

they are just both functions of time

Ive just never come across two independent variables in a Laplace transform before...

there is no unique solution as we don't know any information about the function \(x(t)\)

actually, let me screen shot the probem, perhaps part a and b might be related. Give us a tick

are you doing control theory ?

yep process control

you solve those as a pair
laplace then normal algebra

pretty sure the equations in "a" and "b" form the system

|dw:1440405030249:dw|

i might be wrong though as idk abc of process control

right, so when i've formed one equation, i get
4y'+12x=20e^t

is that the way to go?

It seems awkward to put the ICs with the first equation like that

Still if this is a "system" then where's y'?

yea true

Something doesn't seem right here haha

i'll give that a miss then haha

i'll follow the links process, and see if i get an answer.

no wait, it cannot be a system because you cannot have x' = something
and x' = something else

perhaps the initial conditions are misspelt?

i think its pretty straight forward, my answer was y(t)=cosh(t)

my approach was simply taking the derivative of the integral

\[y''-y=0\]

simply plugin y=cosh(t) and check ?

but we are using laplace transforms here

Oh right I forgot about your initial conditions

haha no problem

y(0)=1
y'(0) = 0
y''-y=0

yeah, i'm assuming you have to say that y'(0)=0...

yeah fair call

your simply integrating from 0 to 0

yeah i'm baffled too...

if it helps
\(x = \frac{5}{4}e^t - \frac{9}{4}e^{-3t}\)
\(y = -\frac{1}{4}e^t + \frac{9}{4}e^{-3t}\)

hmm, how did you get to that?

perhaps i'll give it ago now, ive just finished writing the other minor problem down neatly

you'll kick yourself when you see this
Example 4 at bottom of page

which example am i meant to be looking at?

example 4 shows the method
here are my scribbles
there is indeed a snag in this question. the iv for y on P3 of my scribbles is not met but the same iv is not used in the solution
i would love to understand why this as the solution just feels right but has this issue
is it a problem with the question or have i messed up some stupid algebra?
i really hope this helps rather than hinders

yeah right, thats very interesting. its just the IV's that don't check hey

snag*

hi @chris00
i'm baffled.
would love to know how you eventually come out on this

i'll let you guys know later on in the week when i have a tute on this. cheers guys