(1 point) Use the Laplace transform to solve the following initial value problem:
y'' - 4y' + 5y = 0, y(0) = 0, y'(0) = 1
First, using Y for the Laplace transform of y(t), i.e., Y = L{y(t)}, find the equation you get by taking the Laplace transform of the differential equation
(s^2Y - s - 2) - 4(sY - 1) + 5Y = 0
Now solve for Y(s) =
By completing the square in the denominator and inverting the transform, find
y(t) = e^(2t)sin(t)
(1 point) Use the Laplace transform to solve the following initial value problem:
y'' - 4y' + 5y = 0
y(0) = 0, y'(0) = 1
First, using Y for the Laplace transform of y(t), i.e., Y = L{y(t)}, find the equation you get by taking the Laplace transform of the differential equation
(s^2Y - s - 2 - 4(sY - 1) + 5Y = 0
Now solve for Y(s) = (s - 2)/((s - 2)^2 + 1)
By completing the square in the denominator and inverting the transform, find
y(t) = e^(2t)sin(t)