Question

Solution of
y'+6y+3x=8e^t for y(0)=-1, x(0)=0 using Laplace transofrms

Answer 1

@Empty

Answer 2

I am stuck when im at this stage:

\[Y(s)(s+6)+3X(s)=\frac{ 8-s(s-1) }{ s-1 }\]

Answer 3

i can't seem to use the initial condition of x(0)=0... i'm not sure if theres a unique solution to this question

Answer 4

you've got 2 different variables in there? y and x

so y = x', yes?

Answer 5

how does y=x'?

Answer 6

they are just both functions of time

Answer 7

what i am saying is that this would make more sense if that were true

but i do not have sight of the original question to confirm

if they are independent functions, what are you solving for. don't you need another equation in x and y?

Answer 8

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

Answer 9

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

Answer 10

if you have another equation, then we can solve the system by elimination and get an unique solution \((x(t),y(t))\)

Answer 11

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

Answer 12

basically it is like solving an equation with many unknowns,

there always exist infinitely many solutions when you have more variables but less equations

Answer 13

are you doing control theory ?

Answer 14

yep process control

Answer 15

you solve those as a pair

laplace then normal algebra

Answer 16

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

Answer 17

ah, i thought they would be two seperate problems, but since the first didn't make sense, i was querying things.