Using the definition of the Laplace transform, find the Laplace transform of:
- f(t) = 0, for 0 < t < 1
- f(t) = t, for 1 < t < 2
- f(t) = t^2, for t > 2
Using the definition of the Laplace transform, find the Laplace transform of:
- f(t) = 0, for 0 < t < 1
- f(t) = 1, for 1 < t < 2
- f(t) = t, for t > 2
Find the inverse Laplace transform of: (s^2 + 5 + 2)(s + 4)
Find the inverse Laplace transform of: (s^2 + 4s + 8)
Using the Laplace transform, solve x' + x = 2t, x(0)
Using the Laplace transform, solve x'' + x sin(t) = x(0)