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
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)
Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga.
Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus.
Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
Not the answer you are looking for? Search for more explanations.
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 ...
Where did you get xcos from?
right so for part 3 you meant to solve in terms of x !