Question

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.

Answer 1

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^-1{f(s)} to get y.

Answer 2

There is no y(0) givien, so I'm not sure how to go from there.