Asked by Emily
Use the Laplace Transform to solve this initial value problem.
y'''' - 8y = 0, y'(0)=63, y''(0)=216, y'''(0)=297
I would really appreciate the help.
y'''' - 8y = 0, y'(0)=63, y''(0)=216, y'''(0)=297
I would really appreciate the help.
Answers
Answered by
Steve
Since L{f''''} = s^4 f - s^3f(0) - s^2f'(0) - sf''(0) - f'''(0)
= s^4 f(s) - s^3 f(0) - 63s^2 - 216s - 297
we have
s^4 f(s) - s^3 f(0) - 63s^2 - 216s - 297 - 8f(s) = 0
I think we need y(0) to finish the solution.
(s^4-8) f(s) = s^3 f(0) + 63s^2 + 216s + 297
f(s) = (f(0)s^3+63s^2+216s+297)/(s^4-8)
Now just take L<sup>-1</sup>{f(s)} to get y.
= s^4 f(s) - s^3 f(0) - 63s^2 - 216s - 297
we have
s^4 f(s) - s^3 f(0) - 63s^2 - 216s - 297 - 8f(s) = 0
I think we need y(0) to finish the solution.
(s^4-8) f(s) = s^3 f(0) + 63s^2 + 216s + 297
f(s) = (f(0)s^3+63s^2+216s+297)/(s^4-8)
Now just take L<sup>-1</sup>{f(s)} to get y.
Answered by
Emily
There is no y(0) givien, so I'm not sure how to go from there.