# Laplace transform with step function

## Homework Statement

$$y'+2y=f(t), y(0)=0, where f(t)=\left\{t, 0\leq t<0 \;and \; 0, t \geq 0$$ (I don't know how to do piecewise)

## Homework Equations

Equation for initial conditions; step function: u(t-a)

## The Attempt at a Solution

I know how to solve a differential equation with initial conditions using Laplace transforms, I just don't know what f(t) looks like as a step function, or how it would behave. would it be t*u(t-1)?

hunt_mat
Homework Helper
f(t) looks like 0 for all values of t, are you sure your definition of f(t) is correctly copied down?

Opps, it's:
$$t, \; 0 \leq t < 1$$
$$0, \; t \geq 1$$

hunt_mat
Homework Helper
OKay, then when taking the Laplace transform of the RHS, split the domain of integration to (0,1) and [1, infintity], the part where you integrate over 0 to infinity will vanish and you will be left with:
$$\int_{0}^{1}te^{-st}dt$$