Thread: One more Laplace/initial value question for class tomorrow!!!

Solve the given initial value problem by Laplace transforms. Show te details of your work.

y" - 2y' + 2y = 8e^(-t)(cos t) ; y(0) = 16; y'(0) = 16


I have some of the problem done, but I am not sure that I am doing it right. I am supposed to present this at 1pm tomorrow during class, so any help before then would be greatly appreciated.

Originally Posted by Hollysti

Solve the given initial value problem by Laplace transforms. Show te details of your work.

y" - 2y' + 2y = 8e^(-t)(cos t) ; y(0) = 16; y'(0) = 16


I have some of the problem done, but I am not sure that I am doing it right. I am supposed to present this at 1pm tomorrow during class, so any help before then would be greatly appreciated.

Take the Laplace transform of the equation:

s^2 Y(s) -sy(0) - y'(0) -2[s Y(s) - y(0)] + 2Y(s) = 8 (s+1)/[(s+1)^2+1]

(s^2 -2s +2)Y(s) = 8 (s+1)/[(s+1)^2+1] + 16s - 16

So (if I have done this right)

Y(s) = 8(2s^3 + 2s^2 + s - 3)/[(s^2 + 2·s + 2)(s^2 - 2·s + 2)].

To finish this expand the left hand side in partial fractions and look up the
corresponding inverse LTs to get the solution.

RonL

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