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John_henderson
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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
xdy/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)
 one year ago
 one year ago
John_henderson Group Title
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 xdy/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)
 one year ago
 one year ago

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John_henderson Group TitleBest ResponseYou've already chosen the best response.0
im i supposed to diffrentiate the first part?
 one year ago

John_henderson Group TitleBest ResponseYou've already chosen the best response.0
i dont have a clue how to start this ?
 one year ago

John_henderson Group TitleBest ResponseYou've already chosen the best response.0
How can eliminate x(t)?
 one year ago

John_henderson Group TitleBest ResponseYou've already chosen the best response.0
Any idea how?
 one year ago

slaaibak Group TitleBest ResponseYou've already chosen the best response.0
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.
 one year ago

slaaibak Group TitleBest ResponseYou've already chosen the best response.0
I've never done differential equations or laplace transformations, so I can't help on the second and third one, sorry
 one year ago

John_henderson Group TitleBest ResponseYou've already chosen the best response.0
oh right i see, i think i can do question 2, but not sure about 3?
 one year ago

slaaibak Group TitleBest ResponseYou've already chosen the best response.0
If you give me the answer to the second one, I can try and figure out 3.
 one year ago

John_henderson Group TitleBest ResponseYou've already chosen the best response.0
let me work on ...
 one year ago

mahmit2012 Group TitleBest ResponseYou've already chosen the best response.0
dw:1354568179841:dw
 one year ago

mahmit2012 Group TitleBest ResponseYou've already chosen the best response.0
dw:1354568287483:dw
 one year ago

John_henderson Group TitleBest ResponseYou've already chosen the best response.0
Where did you get xcos from?
 one year ago

mahmit2012 Group TitleBest ResponseYou've already chosen the best response.0
dw:1354568458794:dw
 one year ago

mahmit2012 Group TitleBest ResponseYou've already chosen the best response.0
dw:1354568607205:dw
 one year ago

John_henderson Group TitleBest ResponseYou've already chosen the best response.0
right so for part 3 you meant to solve in terms of x !
 one year ago
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