Question

1. Given that X=x(t) and y=Y(t) are two functions of time, t and they are related by the following equations.

dx/dt - x +y=e^t
x-dy/dt=0

by eliminatiing x=x(t) and its derivative show that : d^2y/dt^2- dy/dt+y = e^t

2. Use laplace transform to solve the resulting differential eqaution :

d^2y/dt^2 - dy/dt +y = e^t

conditions y(0)=1 and dy/dt=1 and t=0

3. Hence find an explicit form of x=x(t)

Answer 1

im i supposed to diffrentiate the first part?

Answer 2

i dont have a clue how to start this ?

Answer 3

How can eliminate x(t)?

Answer 4

Any idea how?

Answer 5

First derive the second equation wrt time:

dx/dt - d^2y/dt^2=0

Rewrite as: dx/dt = d^2y/dt^2 <---- 1

Now rewrite the second equation: x = dy/dt <----2

Now look at the first equation:

dx/dt - x +y=e^t

Sub in 1 and 2:

d^2y/dt^2 - dy/dt + y = e^t

which gives the desired result.

Answer 6

I've never done differential equations or laplace transformations, so I can't help on the second and third one, sorry

Answer 7

oh right i see, i think i can do question 2, but not sure about 3?

Answer 8

If you give me the answer to the second one, I can try and figure out 3.

Answer 9

let me work on ...