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)

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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 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)

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im i supposed to diffrentiate the first part?
i dont have a clue how to start this ?
How can eliminate x(t)?

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Any idea how?
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.
I've never done differential equations or laplace transformations, so I can't help on the second and third one, sorry
oh right i see, i think i can do question 2, but not sure about 3?
If you give me the answer to the second one, I can try and figure out 3.
let me work on ...
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Where did you get xcos from?
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right so for part 3 you meant to solve in terms of x !

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