Solving Diff EQ using a Laplace Transform

[G01]

Homework Statement

Solve the initial value problem:

\frac{dy}{dt} + 2y = u_2(t)e^{-t}

y(0) = 3

Where u_2(t) is a Heaviside Function with the discontinuity at t=2.

Homework Equations

The Laplace transform of a Heaviside function multiplied by another function:

L( u_a(t)f((t-a) ) = e^{-as}L(f(t-a)) Where L denotes the laplace tranform of a function.

The Attempt at a Solution

I know that in order to solve this equations using a laplace transform, I need to convert the RHS to the form of function in part 2. above. Once I do that I can take the Laplace Transform of both sides and then solve for L(y) and then y. I've been working at this for a while now, and I'm stuck on converting the RHS into a function whose transform I know. If I get this, then I can definitely do the rest of the problem. Any hints of converting this function into a workable form will be greatly appreciated.

 

[G01]

Figured it out! Thanks anyway!