- #1

- 131

- 22

## Homework Statement

Solve ##\frac{dy}{dt} -y = 1, y(0) = 0## using the laplace transform

## Homework Equations

## The Attempt at a Solution

##\mathcal{L}\big\{\frac{dy}{dt}\big\} - \mathcal{L}\big\{y\big\} = \mathcal{L}\big\{1\big\}##

##sY(s) - y(0) - \frac{1}{s^2} = \frac{1}{s}##

##Y(s) =\frac{1}{s^3} + \frac{1}{s^2} ##

Applying the inverse Laplace leads to:

##y(t) = \frac{1}{2}t^2 + t##

Which is nothing like the answer obtained with separation of variables. What have I done wrong here?