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anonymous
 3 years ago
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)
anonymous
 3 years ago
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)

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anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0im i supposed to diffrentiate the first part?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0i dont have a clue how to start this ?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0How can eliminate x(t)?

slaaibak
 3 years ago
Best ResponseYou've already chosen the best response.0First 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.

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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0oh right i see, i think i can do question 2, but not sure about 3?

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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0dw:1354568179841:dw

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0dw:1354568287483:dw

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Where did you get xcos from?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0dw:1354568458794:dw

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0dw:1354568607205:dw

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0right so for part 3 you meant to solve in terms of x !
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