Laplace transform applied to a differential equation

[Lord Anoobis]

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?

 

[Lord Anoobis]

Okay, I see the trouble. Made an error with $\mathcal{L}\big\{y\big\}$. Problem solved